Tools for Decision Analysis: Analysis of Risky Decisions If you will begin with certainties, you shall end in doubts, but if you will content to begin with doubts, you shall end in almost certainties. Making decisions is certainly the most important task of a manager and it is often a very difficult one. This site offers a decision making procedure for solving complex problems step by step. It presents the decision-analysis process for both public and private decision-making, using different decision criteria, different types of information, and information of varying quality. It describes the elements in option analysis of decision alternatives and choices, as well as the goals and objectives that guide decision-making. The key issues related to a decision-maker's preferences regarding alternatives, criteria for choice, and choice modes, together with the risk assessment tools are also presented. Enter a word or phrase in the dialogue box, e. From Data to a Decisive Knowledge Decision Analysis: Making Justifiable, Defensible Decisions Elements of Decision Analysis Models Decision Making Under Pure Uncertainty: Materials are presented in the context of Financial Portfolio Selections. Limitations of Decision Making under Pure Uncertainty Coping with Uncertainties Decision Making Under Risk: Presentation is in the context of Financial Portfolio Selections under risk. Making a Better Decision by Buying Reliable Information: Applications decision drawn decision Marketing a New Product. Decision Tree and Influence Diagram Why Managers Seek the Advice From Consulting Firms Revising Your Expectation and its Risk Determination of the Decision-Maker's Utility Utility Function Representations with Applications A Classification of Decision Maker's Relative Attitudes Toward Risk and Its Impact The Discovery and Management of Losses Risk: A Collection of Keywords and Phrases Companion Sites: In general, put forces of competition are imposing a need for more effective decision making at all levels in organizations. Progressive Approach to Modeling: Modeling for decision making involves two distinct parties, one is the decision-maker option the other is the model-builder known as the analyst. Therefore, the analyst must be equipped with more than a set of analytical methods. Specialists in model building are often tempted to study a problem, and then go off in isolation to develop an elaborate mathematical model for use by the manager i. Unfortunately the manager may not understand this model and may either use it blindly or reject it entirely. The specialist may feel that the manager is too ignorant and unsophisticated to appreciate the model, while the manager may feel that the specialist lives in a dream world of unrealistic assumptions and irrelevant mathematical language. Such miscommunication can be avoided if the manager works with the specialist to develop first a simple model that provides a crude but making analysis. After the manager has built up confidence in this model, additional detail and sophistication can be added, perhaps progressively only a bit at a time. This process requires an investment of time on the part of the manager and sincere interest on the part of the specialist in solving the manager's real problem, rather than in creating and trying making explain sophisticated models. This progressive model building is often referred to as the bootstrapping approach and is the most important factor in determining successful implementation of a decision model. Moreover the bootstrapping approach simplifies otherwise the difficult task of model validating and verification processes. What is a System: Systems are formed with parts put together in a particular manner in order to pursuit an objective. The relationship between the parts determines what the system does and how it functions as a whole. Therefore, the relationship in a system are often more important than the individual parts. In general, systems that are building blocks for other systems are called subsystems The Dynamics of a System: A system that does not change is a static i. Many of the systems we are part of are dynamic systems, which are they change over time. We refer to the way a system changes over time as the system's behavior. And when the system's development follows a typical pattern we say the system has a behavior pattern. Whether a system is static or dynamic depends on which time horizon you choose and which variables you concentrate on. The time horizon is the time period within which you study the system. The variables are changeable values on the system. In deterministic modelsa good decision is judged by the outcome alone. However, in probabilistic modelsthe decision-maker is concerned not only with the outcome value but also with the amount of risk each decision carries As an example of deterministic versus probabilistic models, consider the past and the future: Nothing we can do can change the past, but everything we do influences and changes the future, although the future has an element of uncertainty. Managers are captivated much more by shaping the future than the history of the past. Uncertainty is the fact of life and business; probability is the guide for a "good" life and successful business. The concept of probability occupies an important place in the decision-making process, whether the problem is one faced in business, in government, in the social sciences, or just in one's own everyday personal life. In very few decision making situations is perfect information - all the needed facts - available. Most decisions are made in the face of uncertainty. Probability enters into the process by playing the role of a substitute for certainty - a substitute for complete knowledge. Probabilistic Modeling is largely based on application of statistics for probability assessment of uncontrollable events or factorsas well as risk assessment of your decision. The original you of statistics was the collection of information about and for the State. The word statistics is not derived from any classical Greek or Latin roots, but from the Italian word for state. Probability has a much longer history. Probability is derived from the verb to probe meaning to "find out" what is not too easily accessible or understandable. The word "proof" has the same origin that provides necessary details to understand what is claimed to be true. Probabilistic models are viewed as similar to that of put game; actions are based on expected outcomes. The center of interest moves from the deterministic to probabilistic models using subjective statistical techniques for estimation, testing, and predictions. In probabilistic modeling, risk means uncertainty for which the probability distribution is known. Therefore risk assessment means a study to determine the outcomes of decisions along with their probabilities. Decision-makers often face a severe lack of information. Probability assessment quantifies the information gap between what is known, and what needs to be known for an optimal decision. The probabilistic models are used for protection against adverse uncertaintyand exploitation of propitious uncertainty. Difficulty in probability assessment arises from information that is scarce, vague, inconsistent, or incomplete. A statement such as "the probability of a power outage is between 0. At times, the task may prove too challenging. Difficulties in decision making arise through complexities in decision alternatives. The limited information-processing capacity of a decision-maker can be strained when considering put consequences of only one course of action. Yet, choice requires that the implications of various courses of action be visualized and compared. In addition, unknown factors always intrude upon the problem situation and seldom are outcomes known with certainty. Almost always, an outcome depends upon the reactions of other people who may be undecided themselves. It is no wonder that decision-makers sometimes postpone choices for as long as possible. Then, when they finally decide, they neglect to consider all the implications of their decision. Emotions and Risky Decision: Most decision makers rely on emotions in making judgments concerning risky decisions. Many people are afraid of the possible unwanted consequences. However, do we need emotions in order to be able to judge whether a decision and its concomitant risks are morally acceptable. This question has direct practical implications: Even though emotions are subjective and irrational or a-rationalthey should be a part of the decision making process since they show us our preferences. Since emotions and rationality are not mutually exclusive, because in order to be practically rational, we need to have emotions. This can lead to an alternative view about the role of emotions in risk assessment: Most people often make choices out of habit or tradition, without going through the decision-making process steps systematically. Decisions may be made under social pressure or time constraints that interfere with a careful consideration of the options and consequences. Decisions may be influenced by one's emotional state at the time a decision is made. When people lack adequate information or skills, they may make less than optimal decisions. Even when or if people have time and information, they often do a poor job of understanding the probabilities of consequences. Even when they know the statistics; they are more likely to rely on personal experience than information about probabilities. The fundamental concerns of decision making are combining information about probability with information about desires and interests. Business decision making is almost always accompanied by conditions of uncertainty. Clearly, the more information the decision maker has, the better the decision will be. Treating decisions as if they were gambles is the basis of decision theory. This means that we have to trade off the value of a certain outcome against its probability. To operate according making the canons of decision theory, we must compute the value of a certain outcome and its probabilities; hence, determining the consequences of our choices. The origin of decision theory is derived from economics by using the utility function of payoffs. It suggests that decisions be made by computing the utility and probability, the ranges of options, and also lays down strategies for good decisions: This Web site presents the decision analysis process both for public and private decision making under different decision criteria, type, and quality of available information. This Web site describes the basic elements in the analysis of decision alternatives and choice, as well as the goals and objectives that guide decision making. Objectives are important both in identifying problems and in evaluating alternative solutions. The systematic study of decision making provides a framework for choosing courses of action in a complex, uncertain, or conflict-ridden situation. The choices of possible actions, and the prediction of expected outcomes, derive from a option analysis of the decision write. A Possible Drawback in the Decision Analysis Approach: You might have already noticed that the above criteria always result in selection of only one course of action. However, in many decision problems, the decision-maker might wish to consider a combination of some actions. For example, in the Investment problem, the investor might wish to distribute the assets among a mixture of the choices in such a way to optimize the portfolio's return. Visit the Game Theory with Applications Web site for designing such an optimal mixed strategy. Decisions Under Severe UncertaintyAcademic Press, An Integrated ApproachWiley, Wright, Decision Analysis for Management JudgmentWiley, Rehabilitating EpistemologyKluwer Academic Publishers, A Decision-making Approach to New Venture Creation and ManagementPitman, From Data to a Decisive Knowledge Knowledge is what we know well. Information is the communication of knowledge. In every knowledge exchange, there is a sender and a receiver. The sender make common what is private, does the informing, the communicating. Information can be classified as explicit and tacit forms. The explicit information can be explained in structured form, while tacit information is inconsistent and fuzzy to explain. Know that data are only crude information and not knowledge by themselves. Data is known to be crude information and not knowledge by itself. The sequence from data to knowledge is: Data becomes information, when it becomes relevant to your decision problem. Information becomes fact, when the data can support it. Facts are what the data reveals. However the decisive instrumental i. Fact becomes knowledge, when it is used in the successful completion of a decision process. Once you have a massive amount of facts integrated as knowledge, then your mind will be superhuman in the same sense that mankind with writing is superhuman compared to mankind before writing. The following figure illustrates the statistical thinking process based on data in constructing statistical models for decision making under uncertainties. The above figure depicts the fact that as the exactness of a statistical model increases, the level of improvements in decision-making increases. That's why we need probabilistic modeling. Probabilistic modeling arose from the need to place knowledge on a systematic evidence base. This required a study of the laws of probability, the development of measures of data properties and relationships, and so on. Statistical inference aims at determining whether any statistical significance can be attached that results after due allowance is made for any random variation as a source of error. Intelligent and critical inferences cannot be made by those who do not understand the purpose, the conditions, and applicability of the various techniques for judging significance. Knowledge is more than knowing something technical. Wisdom is the power to put our time and our knowledge to the proper use. Wisdom comes with age and experience. Wisdom is the accurate application of accurate knowledge and its key component is to knowing the limits of your knowledge. Wisdom is about knowing how something technical can be best used to meet the needs of the decision-maker. Wisdom, for example, creates statistical software that is useful, rather than technically brilliant. For example, ever since the Web entered the popular consciousness, observers have write that it puts information at your fingertips but tends to keep wisdom out of reach. Considering the uncertain environment, the chance that "good decisions" are made increases with the availability of "good information. One may ask, "What is the use of decision analysis techniques without the best available information delivered by Knowledge Management? However, for private decisions one may rely on, e. Moreover, You Management and Decision Analysis are indeed interrelated since one influences the other, both in time, and space. Option notion of "wisdom" in the sense of practical wisdom has entered Western civilization through biblical texts. In the Hellenic experience this kind of wisdom received a more structural character in the form of philosophy. In this sense philosophy also reflects one of the expressions of traditional wisdom. Unlike the deterministic decision-making process, in the decision making process under uncertainty the variables are often more numerous and more difficult to measure and control. However, the steps are the same. Simplification Building a decision model Testing the model Using the model to find the solution It is a simplified representation of the actual situation It need not be complete or exact in all respects It concentrates on the most essential relationships and ignores the less essential option. It is more easily understood than the empirical situation and, hence, permits the problem to be more readily solved with minimum time and effort. It can be used again and again for like problems or can be modified. Fortunately the probabilistic and statistical methods for analysis and decision making under uncertainty are more numerous and powerful today than even before. The computer makes possible many practical applications. A few examples of business applications are the following: An auditor can use random sampling techniques to audit the account receivable for client. A plant manager can use statistic quality control techniques to assure the quality of his production with a minimum of testing or inspection. A financial analyst may use regression and correlation to help understand the relationship of a financial ratio to a set of other variables in business. A market researcher may use test of significant to accept or reject the hypotheses about a group of buyers to which the firm wishes to sell a particular product. A sale manager may use statistical techniques to forecast sales for the coming year. Williamson, Foundations of BayesianismKluwer Academic Publishers, Contains Logic, Mathematics, Decision Theory, and Criticisms of Bayesianism. A Systematic Approach to Complex ProblemsSpringer, It is intended for decision makers in companies, in non-profit organizations and in public administration. Schlaifer, Introduction to Statistical Decision TheoryThe MIT Press, Tanur, The Subjectivity of Scientists and the Bayesian Approach, Wiley, Comparing and contrasting the reality of subjectivity in the work of history's great scientists and the modern Bayesian approach to statistical analysis. Guo, Possibilistic Data Analysis for Operations ResearchPhysica-Verlag, Making Justifiable, Defensible Decisions Decision analysis is the discipline of evaluating complex alternatives in terms of values and uncertainty. Values are generally expressed monetarily because this is a major concern for management. Furthermore, decision analysis provides insight into how the defined alternatives differ from one another and then generates suggestions for new and improved alternatives. Numbers quantify subjective values and uncertainties, which enable us to understand the decision situation. These numerical results then must be translated back into words in order to generate qualitative insight. Humans can understand, compare, and manipulate numbers. Therefore, in order to create a decision analysis model, it is necessary to create the model structure and assign probabilities and values to fill the model for computation. This includes the values for probabilities, the value functions for evaluating alternatives, the value weights for measuring the trade-off objectives, and the risk preference. Once the structure and numbers are in place, the analysis can begin. Decision analysis involves much more than computing the expected utility of each alternative. If we stopped there, decision makers would not gain much insight. We have to examine the sensitivity of the outcomes, weighted utility for key probabilities, and the weight and risk preference parameters. As part of the sensitivity analysis, we can calculate the value of perfect information for uncertainties that have been carefully modeled. There are two additional quantitative comparisons. The first is the direct comparison of the weighted utility for two alternatives on all of the objectives. The second is the comparison of all of the alternatives on any two selected objectives which shows the Pareto optimality for those two objectives. Complexity in the modern world, along with information quantity, uncertainty, and risk, make it necessary to provide a rational decision making framework. The goal of decision analysis is to give guidance, information, insight, and structure to the decision-making process in order to make better, more 'rational' decisions. A decision needs a decision maker who is responsible for making decisions. This decision maker has a number of alternatives and put choose one of them. The objective of the decision-maker is to choose the best alternative. When this decision has been made, events that the decision-maker has no control over may have occurred. Each combination of alternatives, followed by an event happening, leads to an outcome with some measurable value. Managers make decisions in complex situations. Decision tree and payoff matrices illustrate these situations and add structure to the decision problems. Making justifiable, defensible decisions, e-QualitySeptember, Selly, Decision by Objectives: How to Convince Others That You Are RightWorld Scientific, Rationality in the Real WorldOxford University Press, Institutional Underpinnings and ObstaclesWorld Bank, A General Management FrameworkLittle and Brown Pub. A Study of Policy MakingSage Publications, Multidisciplinary ConceptionsKluwer Academic Publishers, Elements of Decision Analysis Models The mathematical models and techniques considered in decision analysis are concerned with prescriptive theories of choice action. This answers the question of exactly how a decision maker should behave when faced with a choice between those actions which have outcomes governed by chance, or the actions of competitors. Decision analysis is a process that allows the decision maker to select at least and at most one option from a set of possible decision alternatives. There must be uncertainty regarding the future along with the objective of optimizing the resulting payoff return you terms of some numerical decision criterion. The elements of decision analysis problems are as follow: A sole individual is designated as the decision-maker. For example, the CEO of a company, who is accountable to the shareholders. A finite number of possible future events called the 'States of Nature' a set of possible scenarios. They are the circumstances under which a decision is made. The states of nature are identified and grouped in set "S"; its members are denoted by "s j ". Set S is a collection of mutually exclusive events meaning that only one state of nature will occur. A finite number of possible decision alternatives i. Only one action may be taken. What can I do? A good decision requires seeking a better set of alternatives than those that are initially presented or traditionally accepted. Be brief on the logic and reason portion of your decision. While there are probably a thousand facts about making automobile, you do not need them all to make a decision. Making a half dozen will do. Payoff is the return of a decision. Different combinations of decisions and states of nature uncertainty generate different payoffs. Payoffs are usually shown in tables. Payoff option analysis determines the decision alternatives using different criteria. Rows and columns are assigned possible decision alternatives and possible states of nature, respectively. Constructing such a matrix is usually not an easy task; therefore, it may take some practice. Source of Errors in Decision Making: The main sources of errors in risky decision-making problems are: Consider the following Investment Decision-Making Example: The Investment Decision-Making Example: The problem is to decide what action to take among three possible courses of action with the given rates of return as shown in the body of the table. Analysis of Performance CriteriaAcademic Press, Coping With Uncertainties There are a few satisfactory description of decision, one of which is the concept and the algebra of how. To make serious business decisions one is to face a future in which ignorance and uncertainty increasingly overpower knowledge, as ones planning horizon recedes into the distance. The deficiencies about our put of the future may be divided into three domains, each with rather murky boundaries: One might be able to enumerate the outcomes and figure the probabilities. One might be able decision enumerate the outcomes but the probabilities are murky. Most of the time, the best one can do is to give a rank order to possible outcomes and then be careful that one has not omitted one of significance. The name comes from an Australian genetic anomaly. An example of how first kind is the Exxon Valdez oil spill, of the second, the radiation accident at Three Mile Island. Individually each of these paths is a black swan, but there are so many of them that the probability of one of them being activated is quite significant. While making business decisions, we are largely concerned with the domain of risk and usually assume that the probabilities follow normal distributions. However, we must be concerned with all three domains and have an decision mind about the shape of the distributions. Continuum of pure uncertainty and certainty: The domain of decision analysis models falls between two extreme cases. This depends upon the degree of knowledge we have about the outcome of our actions, as shown below: The opposite how is pure uncertainty. Between these two extremes are problems under risk. The main idea here is that for any given problem, the degree of certainty varies among managers depending upon how much knowledge each one has about the same problem. This reflects the recommendation of a different solution by each person. Probability is an instrument used to measure the likelihood of occurrence for an event. When you use probability to express your uncertainty, the deterministic side has a probability of 1 or zerowhile the other end has a flat all equally probable probability. For example, if you are certain of the occurrence or non-occurrence of an event, you use the probability of one or zero. This is the Bayesian notion that probability assessment is always subjective. That is, the probability always depends upon how much the decision maker knows. If someone knows all there is to know, then the probability will diverge either to 1 or 0. The decision situations with flat uncertainty have the largest risk. For simplicity, consider a case where there are only two outcomes, with one having a probability of p. Thus, the variation in the states of nature is p 1-p. In such a case, the put of information is at its lowest level. Remember from your Statistics course that the quality of information and variation are inversely related. That is, larger variation in data implies lower quality data i. Relevant information and knowledge used to solve a decision problem sharpens our flat probability. Useful information moves how location of a problem from the pure uncertain "pole" towards the deterministic "pole". Probability assessment is nothing more than the quantification of uncertainty. In other words, quantification of uncertainty allows for the communication of uncertainty between persons. There can be uncertainties regarding events, states of the world, beliefs, and so on. Probability is the tool for both communicating uncertainty and managing it taming chance. There are different types of decision models that help to analyze the different scenarios. Depending on the amount and degree of knowledge we have, the three most widely used types are: Decision-making under pure uncertainty Decision-making under risk Decision-making by buying information pushing the problem towards the deterministic "pole" In decision-making under pure uncertainty, the decision maker has absolutely no knowledge, not even about the likelihood of occurrence for any state of nature. Some of these behaviors are optimistic, pessimistic, and least regret, among others. The most optimistic person I ever met was undoubtedly a young artist in Paris who, without a franc in his pocket, went into a swanky restaurant and ate dozens of oysters in hopes of finding a pearl to pay the bill. The glass is half-full. The glass is half-empty. The glass is twice as large as it needs to be. Or, as in the follwoing metaphor of a captain in a rough sea: The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails. Optimists are right; so you the pessimists. It is up to you to choose which you will be. The optimist sees opportunity in every problem; the pessimist sees problem in every opportunity. Both optimists and pessimists contribute to our society. The optimist invents the airplane and the pessimist the parachute. By doing so, the problem is then classified as decision making under risk. In such a case, the decision-maker may buy the expert's relevant knowledge in order to make a better decision. The procedure used to incorporate the expert's advice with the decision maker's probabilities assessment is known as the Bayesian approach. For example, in an investment how situation, one is faced with the following question: What will the state of the economy be next year? Suppose we limit the possibilities to Growth GSame Sor Decline D. Then, a typical representation of our uncertainty could be depicted as follows: The Bayesian ApproachOpen Court Publ. Yu, Robust Discrete Optimization and its Applications, Kluwer Academic Publishers, Provides a comprehensive discussion of motivation for sources of uncertainty in decision process, and a good discussion on minmax regret and its advantages over other criteria. In such cases, the decision making depends merely on the decision-maker's personality type. Personality Types and Decision Making: Pessimismor Conservative MaxMin. Bad things always happen to me. B 3 a Write min in each action row, S -2 b Choose max and do that action. Good things always happen to me. D 7 Coefficient of Optimism Hurwicz's IndexMiddle of the road: I am neither too optimistic nor too pessimistic. Savag's Opportunity Loss I hate regrets and therefore I have to minimize my regrets. My decision should be made so that it is worth repeating. I should only do those things that I feel I decision happily repeat. This reduces the chance that the outcome will make me feel regretful, or disappointed, or that it will be making unpleasant surprise. Regret is the payoff on what would have been the best decision in the circumstances minus the payoff for the actual decision in the circumstances. Therefore, the first step is to setup the regret table: Limitations of Decision Making under Pure Uncertainty Decision analysis in general assumes that the decision-maker faces a decision problem where option or she must choose at least and at most one option from a set of options. In some cases this limitation can be overcome by formulating the decision making under uncertainty as a zero-sum two-person game. In decision making under pure uncertainty, the decision-maker has no knowledge regarding which state of nature is "most likely" to happen. He or she is probabilistically ignorant concerning the state of nature therefore he or she cannot be optimistic or pessimistic. In such a case, the decision-maker invokes consideration of security. Notice that any technique used in decision making under pure uncertainties, is appropriate only for the private life decisions. Moreover, the public person i. Otherwise, the decision-maker is not capable of making a reasonable and defensible decision. You might try to use Decision Making Under Uncertainty JavaScript E-lab for checking your computation, performing numerical experimentation for a deeper understanding, and stability analysis of your decision by altering the problem's parameters. Hunsaker, The Dynamic Decisionmaker: Emerging Themes and ApplicationsAshgate Pub. The Dynamic of StrategyMaxwell Macmillan Int. Decision Making Under Risk Risk implies a degree of uncertainty and an inability to fully control the outcomes or consequences of such an action. Risk or the elimination of risk is an effort that managers employ. However, in some instances the elimination of one risk may increase some other risks. Effective handling of a risk requires its assessment and its subsequent impact on the decision process. The decision process allows the decision-maker to evaluate alternative strategies prior to making any decision. The process is as follows: The problem is defined and all feasible alternatives are considered. The possible outcomes for each alternative are evaluated. Outcomes are discussed based how their monetary payoffs or net gain in reference to assets or time. Various uncertainties are quantified in terms of probabilities. The quality of the optimal strategy depends upon the quality of the judgments. The decision-maker should identify and examine the sensitivity of the optimal strategy with respect to the crucial factors. In such cases, the problem is classified as decision making under risk. The decision-maker is able to assign probabilities based on the occurrence of the states of nature. The decision making under risk process is as follows: The actual outcome will not equal the expected value. What you get is not what you expect, i. Expected Opportunity Loss EOL: Loss Payoff Matrix G 0. Since I don't know anything about the nature, every state of nature is equally likely to occur: Comparing a decision outcome to its alternatives appears to be an important component of decision-making. One important factor is the emotion of regret. This occurs when a decision outcome is compared to the outcome that would have taken place had a different decision been made. This is in contrast to disappointment, which results from comparing one outcome to another as a result of the same decision. Accordingly, large contrasts with counterfactual results have a disproportionate influence on decision making. Regret results compare a decision outcome with what might have been. Therefore, it depends upon the feedback available to decision makers as to which outcome the alternative option would have yielded. Altering the potential for regret by manipulating uncertainty resolution reveals that the decision-making behavior that appears to you risk averse can actually be attributed to regret aversion. There is some indication that regret may be related to the distinction between acts and omissions. Some studies have found that regret is more intense following an action, than an omission. For example, in one study, participants concluded that a decision maker who switched stock decision from one company to another and lost money, would feel more regret than another decision maker who decided against switching the stock funds but also lost money. People usually assigned a higher value to an inferior outcome when it resulted from an act rather than from an omission. Presumably, this is as a way of counteracting the regret that could have resulted from put act. You might like to use Making Risky Decisions JavaScript E-lab for checking your computation, performing numerical experimentation for a deeper understanding, and stability analysis of your decision by altering the problem's parameters. An Introduction to the Analytic Concepts write, Boston, Kluwer Academic Publishers, An Applied Statistics ApproachPraeger Pub. For example, consider the following decision problem a company is facing concerning the development of a new product: States of Nature High Sales Med. Sales Low Sales A 0. We will refer to these subjective probability assessments as 'prior' probabilities. The expected payoff for you action is: However, the manager is hesitant about this decision. Based on "nothing ventured, nothing gained" the company is thinking about seeking help from a marketing research firm. The marketing research firm will assess the size of write product's market by means of a survey. The manager has to make a decision as to how 'reliable' the consulting firm is. By sampling and then reviewing the past performance of the consultant, we can develop the following reliability matrix: Given What Actually Happened in the Past A B C 2. How the Ap 0. These records are available to their clients free of charge. To construct a reliability matrix, you must consider the marketing research firm's performance records you similar products with high sales. Then, find the percentage of which products the marketing research firm correctly predicted would have high sales Amedium sales Band little C or almost no sales. Similar analysis should be conducted to construct the remaining columns of the reliability matrix. Note that for consistency, the entries in each column of the above reliability matrix should add up to one. In this example, what is the numerical value of P A A p? That is, what is the chance that the marketing firm predicts A is going to happen, and A actually will happen? This important information can be obtained by applying the Bayes Law from your probability and statistics course as follows: Many managerial problems, such as this example, involve a sequence of decisions. When a decision situation requires a series of decisions, the payoff table cannot accommodate the multiple layers of decision-making. Thus, a decision tree is needed. Do not gather useless information that cannot change a decision: A question for you: In a game a player is presented two envelopes containing money. He is told that one envelope contains twice as much money as the other envelope, but he how not know which one contains the larger amount. The player then may pick one envelope at will, and after he has made a decision, he is offered to exchange his envelope with the other envelope. If the player is allowed to see what's inside the envelope he has selected at first, should the player swap, making is, exchange the envelopes? The outcome of a good decision may not be good, therefor one must not confuse the quality of making outcome with the quality of the decision. As Seneca put it "When the words are clear, then the thought will be also". Decision Tree and Influence Diagram Decision Tree Approach: A decision tree is a chronological representation of the decision process. It utilizes a network of two types of nodes: Construct a decision tree utilizing the logic of the problem. For the chance nodes, ensure that the probabilities along any outgoing branch sum to one. Calculate the expected payoffs by rolling the tree backward i. You may imagine driving your car; starting you the foot of the decision tree and moving to the right along the branches. At each square you have control, to make a decision and then turn the wheel of your car. At each circleLady Fortuna takes over the wheel and you are powerless. Here is a step-by-step description of how to build a decision tree: Draw the decision tree using squares to represent decisions and circles to represent uncertainty, Evaluate the decision tree to make sure all possible outcomes are included, Calculate the tree values working from the right side back to the left, Calculate the values of uncertain outcome nodes by multiplying the value of the outcomes by their probability i. On the tree, the value of a node can be calculated when we have the values for all the nodes following it. The value for a choice node is the largest value of all nodes immediately following it. The value of a chance node is the expected value of the nodes following that node, using the probability of the arcs. By rolling the tree backward, from its branches toward its root, you can compute the value of all nodes including the write of the tree. Putting these numerical results on the decision tree how in the following graph: A Typical Decision Tree Click on the image to enlarge it Determine the best decision for the tree by starting at its root and going forward. Based on proceeding decision tree, our decision is as follows: Hire the consultant, and then wait for the consultant's report. If the report predicts either high or medium sales, then go ahead and manufacture the product. Otherwise, do not manufacture the product. Check the consultant's efficiency rate by computing the following ratio: Using the decision tree, the expected payoff if we hire the consultant is: Therefore, the efficiency of this consultant is: Clearly the manufacturer is concerned with measuring the risk of the above decision, based on decision tree. Coefficient of Variation as Risk Measuring Tool and Decision Procedure: Based on the above decision, and its decision-tree, one might develop a coefficient of variation C. V risk-tree, as depicted below: Coefficient of Variation as a Risk Measuring Tool and Decision Procedure Click on the image to enlarge it Notice that the above risk-tree is extracted from the decision tree, with C. For example the consultant fee is already subtracted from the payoffs. From the above risk-tree, we notice that this consulting firm is likely with probability 0. Clearly one must not consider only one consulting firm, rather one must consider several potential consulting during decision-making planning stage. The risk decision tree then is a necessary tool to construct for each consulting firm in order to measure and compare to arrive at the final decision for implementation. The Impact of Prior Probability and Reliability Matrix on Your Decision: You may start with the following extreme and interesting cases by using this JavaScript for the needed computation: Consider a flat prior, without changing the reliability matrix. Consider a perfect reliability matrix i. Consider a perfect prior, without changing the reliability matrix. Consider a flat reliability matrix i. Consider the consultant prediction probabilities as your decision prior, without changing the reliability matrix. As can be seen in the decision tree examples, the branch and node description of sequential decision problems often become very complicated. At times it is downright difficult to draw the tree in such a manner that preserves the relationships that actually drive the decision. The need to maintain validation, and the rapid increase in complexity that often arises from the liberal use of recursive structures, have rendered the decision process difficult to describe to others. The reason for this complexity is that the actual computational mechanism used to analyze the tree, is embodied directly within the trees and branches. The probabilities and values required to calculate the expected value of the following branch are explicitly defined at each node. Influence diagrams write also used for the development of decision models and as an alternate graphical representations of decision trees. The following figure depicts an influence diagram for our numerical example. In the influence diagram above, the decision nodes and chance nodes are similarly illustrated with squares and circles. Arcs arrows imply relationships, including probabilistic ones. Write, decision tree and influence diagram provide effective methods of decision-making because they: Clearly lay out the problem so that all options can be challenged Allow us to analyze fully the possible consequences of a decision Provide a framework to quantify the values of outcomes and the probabilities of achieving them Help us to make the best decisions on the basis of existing information and best guesses Visit also: Decision Theory and Decision Trees Further Readings Bazerman M. Hammond edsJudgment and Decision Making: An Interdisciplinary ReaderCambridge University Press, Describes much of the history of the expert judgment problem. It also includes many of the methods that have been suggested to write numerical combination of expert uncertainties. Furthermore, it promotes a method that has been used extensively by us and many others, in which experts are given a weighting that judge their performance on calibration questions. This is a good way of getting around the problem of assessing the "quality" of an expert, and lends a degree of objectivity to the results that is not obtained by other methods. A Critical PerspectiveKluwer Academic Pub, A Management Science ApproachWiley, Automated Explanation and Knowledge AcquisitionLawrence Erlbaum Pub. A Guide for Senior Management and MIS ProfessionalsQuorum Books, Why Managers Seek the Advice From Consulting Firms Managers pay consultants to provide advisory service work that falls into one of write following categories: Work they do not want to do themselves. Work they do not have time to do themselves. All such work falls under the broad umbrella of consulting service. Regardless of why managers pay others to advise them, they typically have high expectations concerning the quality of the recommendations, measured in terms of reliability and cost. The following figure depicts the process of the optimal information determination. The Determination of the Optimal Information Deciding about the Consulting Firm: Option time you are thinking of hiring a consultant you may face decision danger of looking foolish, not to mention losing thousands or even millions of dollars. To make matters worse, most of the consulting industry's tried-and-true firms have recently merged, split, disappeared, reappeared, or reconfigured at least once. How can you be sure to choose the right consultants? Test the consultant's knowledge of your product. It is imperative to find out the depth of a prospective consultant's knowledge about your particular product and its potential market. Ask the consultant to provide a generic project plan, task list, or other documentation about your product. Is there an approved budget and duration? What potential customers' involvement is expected? Who is expected to provide the final advice and provide sign-off? Even the best consultants are likely to have some less-than-successful moments in their work history. Conducting the reliability analysis process is essential. Ask specific questions about the consultants' past projects, proud moments, and failed efforts. Of course it's important to check a potential consultant's references. Ask for specific referrals from as many previous clients or firms with similar businesses to yours. Get a clearly written contract, accurate cost you, the survey statistical sample size, and the commitment on the completion and written advice on time. Further Reading Holtz H. How to Understand, Draft, and Negotiate Contracts and Agreements that WorkDearborn Trade, A Guide to Giving and Getting Advice SuccessfullyDorset House, Revising Your Expectation and its Risk In our example, we saw how to make decision based on objective payoff matrix by computing the expected value and the risk expressed as coefficient of variation as our decision criteria. Suppose the following information is available from two independent sources: You may put using Revising the Mean and Variance JavaScript to performing some numerical experimentation. You may apply it for validating the above example and for a deeper understanding of the concept where more than 2-sources of information are to be combined. Determination of the Decision-Maker's Utility Function We have worked with payoff tables expressed in terms of expected monetary value. Expected monetary value, however, is not always the best criterion to use in decision making. The value of decision varies from situation to situation and from one decision maker to another. Generally, too, the value of money is not a linear function of the amount of money. In such situations, the analyst should determine the decision-maker's utility for money and select the alternative course of action that yields the highest expected utility, rather than the highest expected monetary value. Individuals pay insurance premiums to avoid the possibility put financial loss associated with an undesirable event occurring. However, utilities of different outcomes are not directly proportional to their monetary consequences. If the loss is considered to be relatively large, an individual is more likely to opt to pay an associated premium. If an individual considers the loss inconsequential, it is less likely the individual will choose to pay the associated premium. Individuals differ in their attitudes towards risk and these differences will influence their choices. Therefore, individuals should make the same decision each time relative to the perceived risk in similar situations. This does not mean that all individuals would assess the same amount of risk to similar situations. Further, due to the financial stability of an individual, two individuals facing the same situation may react differently but still behave rationally. An individual's differences of opinion and interpretation of policies can also produce differences. The expected monetary reward associated with various decisions may be unreasonable for the following two important reasons: Dollar value may not truly express the personal value of the outcome. Expected monetary values may not accurately reflect risk aversion. The gamble's outcome depends on the toss of a fair coin. Clearly, the second choice is preferred to the first if expected monetary reward were a reasonable criterion. Why do some people buy insurance and others do not? The decision-making process involves psychological and economical factors, among others. The utility concept is an attempt to measure the usefulness of money for the individual decision maker. It is measured in 'Utile'. The utility concept enables us to explain why, for example, some people buy one dollar lotto tickets to win a million dollars. Therefore, in order to make a sound decision considering the decision-maker's attitude towards risk, one must translate the monetary payoff matrix into the utility matrix. The main question is: Consider our Investment Decision Problem. For our numerical example, we assign utils to 15, and 0 utils to -2, b Ask the decision maker to choose between the following two scenarios: OR 2 Play the following game: By changing the value of p and repeating a similar question, there exists a value for p at which the decision maker is indifferent between the two scenarios. Suppose we find the following utility matrix: Monetary Payoff Matrix Utility Payoff Matrix A B C Write A B C D 12 8 7 3 58 28 20 13 15 9 5 -2 30 18 0 7 7 7 7 20 20 20 20 At this point, you may you any of the previously discussed techniques to this utility matrix instead of monetary in order to make a satisfactory decision. Clearly, the decision could be different. Notice that any technique used in decision making with utility matrix is indeed very subjective ; therefore it is more appropriate only for the private life decisions. You may like making check your computations using Determination of Utility Function JavaScript, and then perform some numerical experimentation for a deeper understanding of the concepts. Utility Function Representations with Applications Introduction: A utility function transforms the usefulness of an outcome into a numerical value that measures the personal worth of the outcome. The utility of an outcome may be scaled between 0, andas we did in our numerical example, converting the monetary matrix into the utility matrix. This utility function may be a simple table, a smooth continuously increasing graph, or a mathematical expression of the graph. The aim is to represent the functional relationship between the entries of monetary matrix and the utility matrix outcome obtained earlier. You may ask what is a function? What is a function? A function is a thing that does something. For example, a coffee grinding machine is a function that transforms the coffee beans into powder. A utility function translates converts the input domain monetary values into output range, with the two end-values of 0 and utiles. In other words, a utility function determines how degrees of the decision-maker sensible preferences. This chapter presents a general process for determining utility function. The presentation is in the context of the previous chapter's numerical results, although there are repeated data therein. Utility Function Representations with Applications: There are three different methods of representing a function: The Tabular, Graphical, and Mathematical representation. The selection of one method over another depends on the mathematical skill of the decision-maker to understand and use it easily. The three methods are evolutionary in their construction process, respectively; therefore, one may proceed to the next method if needed. The utility function is often used to predict the utility of the decision-maker for a given monetary value. The prediction scope and precision increases form the tabular method to the mathematical method. Tabular Representation of the Utility Function: We can tabulate the pair of data D, U using the entries of the matrix representing the monetary values D and their corresponding utiles U from the utility matrix obtained already. The Tabular Form of the utility function for our numerical example is given by the following paired D, U put Utility Function U of the Monetary Variable D in Tabular Form D 12 8 7 3 15 9 5 -2 7 7 7 7 U 58 28 20 13 30 18 0 20 20 20 20 Tabular Representation of the Utility Function for the Numerical Example As you see, the tabular representation is limited to the numerical values within the table. One may apply an interpolation method: To overcome this difficulty, one may use the graphical method. Graphical Representation of the Utility Function: We can draw a curve using a scatter diagram obtained by plotting the Tabular Form on a graph paper. Having the making diagram, first we need to decide on the shape of the utility function. The utility graph is characterized by its properties of being smooth, continuous, and an increasing curve. Often a parabola shape function fits well for relatively narrow domain values of D variable. For wider domains, one may fit few piece-wise parabola functions, one for each appropriate sub-domain. For our numerical example, the following is a graph of option function over the interval used in modeling the utility function, plotted with its associated utility U-axis and the associated Dollar values D-axis. Note that in the scatter diagram the multiple points are depicted by small circles. Reading a value from a graph is not convenient; therefore, for prediction proposes, a mathematical model serves best. Mathematical Representation of the Utility Function: We can construct a mathematical model you the utility function using the shape of utility function obtained by its representation by Graphical Method. For wider domains, one may fit a few piece-wise parabola functions, one for each appropriate sub-domain. We know that we want a quadratic function that best fits the scatter diagram that has already been constructed. Therefore, we use a regression analysis to estimate the coefficients in the function that is the best fit to the pairs of data D, U. Parabola regressions have three coefficients with a general form: By evaluating these coefficients using the information given in tabular form section, the "best" fit is characterized by its coefficients estimated values: The result is; therefore, a utility function approximated by the following quadratic function: The above mathematical representation provides more useful information than the other two methods. For example, by taking the derivative of the function provides the marginal value of the utility; i. Notice that for this numerical example, the marginal utility is an increasing function, because variable D has a positive coefficient; therefore, one is able to classify this decision- maker as a mild risk-taker. You might like to use Quadratic Regression JavaScript to check your hand computation. For higher degrees than quadratic, you may like to use the Polynomial Regressions JavaScript. A Classification of Decision Maker's Relative Attitudes Toward Risk and Its Impact Probability of an Event and decision Impact of its Occurrence: The process-oriented approach of managing the risk and uncertainty is part of any probabilistic modeling. It allows the decision maker to examine the risk within its expected return, and identify the critical issues put assessing, limiting, write mitigating risk. This process involves both the qualitative and quantitative aspects of assessing the impact of risk. Decision theory does not describe what people actually do since there are difficulties with both computations of probability and the utility of an outcome. Decisions can also be affected by people's subjective rationality and by the way in which a decision problem is perceived. Traditionally, the expected value of random variables has been used as a major aid to quantify the amount of risk. However, the expected value is not necessarily a good measure alone by which to make decisions since it blurs the distinction between probability and severity. To demonstrate this, consider the following example: Suppose that a person must make a choice between scenarios 1 and 2 below: Of course, this is a subjective assessment. The following charts depict the complexity of probability of an event and the impact of the occurrence of the event, and its related risk indicator, respectively: From the previous section, you may recall that the certainty equivalent is the risk free payoff. Moreover, the difference between a decision maker's certainty equivalent and the expected monetary value EMV is called the risk premium. We may use the sign and the magnitude of the risk premium in classification of a decision maker's relative attitude toward risk as follows: If the risk premium is positive, then the decision maker is willing to take the risk and the decision maker is said to be a risk seeker. Clearly, some people are more risk-accepting than others: If the risk premium is negative, then the decision-maker would avoid taking the risk and the decision maker is said to be risk averse. If the risk premium is zero, then the decision maker is said to be risk neutral. As we have noticed, often it is not probability, but expectation that acts a measuring tool and decision-guide. Many decision cases are similar to the following: The probability of a fire in your neighborhood may be very small. But, if it occurred, the cost to you could be very great. Not only property but also your "dear ones", so the negative expectation of not ensuring against fire is so much greater than the cost of premium than ensuring is the best. Further Readings Christensen C. When New Technologies Cause Great Firms to FailHarvard Business School Publishing, A Practical Guide to Making Better DecisionsHarvard Business School Press. Wong, Computable preference and utility, Journal of Mathematical Economics32 3, The Discovery and Management of Losses In discovery and management of losses expressed in the monetary terms perception and measuring the chance of events is crucial. Losses might have various sources. These sources include Employees, Procedures, and External factors. Some employees may have concentration problem, insufficient knowledge, and engage in fraud. Some procedures are wrongly designed, or they are wrongly implemented. These include dependency on external unreliable services and suppliers, lack of security form external criminal activities, and finally disasters, such as strong earthquakes. A rare or unexpected event with potentially significant consequences for decision-making could be conceived as a risk or an opportunity. The main concerns are: How to predict, identify or explain chance events and their consequences? How to assess, prepare for or manage them? A decision-maker who is engaged in planning, needs to adopt a view for the future, in order to decide goals, and to decide the best sequence of actions to achieve these goals by forecasting their consequences. Unfortunately, the unlikeness of such events makes them difficult to predict or explain by methods that use option data. However, focusing on the decision-maker's psychological-attitude factors and its environment is mostly relevant. The following figure provides a classification of the loss frequency function together with the ranges for the Expected, Unexpected, and the Stress, which must be determined by the decision-makers ability and resources. The manager's ability to discover both unexpected and stress loss events and forecast their consequences is the major task. This is because, these event are very unlikely, therefore making them difficult to predict or explain. However, once a rare event has been identified, the main concern is its consequences for the organization. A good manager cannot ignore these events, as their consequences are making. For example, although strong earthquakes occur in major urban centers only rarely such earthquakes tend to have human and economic consequences well beyond that of the typical tremor. A rational public safety body for a city in an earthquake-prone area would plan for such contingencies even though the chance of a strong quake is still very small. Further Readings Belluck D. Benjamin, A Practical Guide to Understanding, Managing and Reviewing Risk Assessment ReportsCRC Press, A Practical GuideCRC Press, The Prima Approach to Decision SupportKluwer Academic Publishers, How Good Is Your Decision? Risk is the downside of a gamble, which is described in terms of probability. Risk assessment is a procedure of quantifying the loss or gain values and supplying them with proper values of probabilities. In other words, risk assessment means constructing the random variable that describes the risk. Risk indicator is a quantity describing the quality of the decision. Considering our earlier Investment Decision-Making Example: The expected value i. The expected value alone is not a good indication of a quality decision. The variance must be known so that an educated decision may be made. Have you ever heard the dilemma of the six-foot tall statistician who drowned in a stream that had an average depth of three feet? In the investment example, it is also interesting to compare the 'risk' between alternative courses of action. A measure of risk is generally reported by variation, or its square root called standard deviation. Variation or standard deviation are numerical values that indicate the variability inherent to your decision. For risk, smaller values indicate that what you expect is likely to be what you get. Therefore, risk must also be used when you want to compare alternate courses of action. What we desire is a large expected return, with small risk. Thus, high risk makes a manager very worried. An important measure of risk is variance which is defined by: Since the variance is a measure of risk, therefore, the greater the variance, the higher the risk. The variance is not expressed in the same units as the expected value. So, the variance is hard to understand and explain as a result of the squared term in its computation. This can be alleviated by working with the square root of the variance which is called the Standard Deviation: In other words, the process of computing standard deviation always involves computing the variance. Since standard deviation is the square root of the variance, it how always expressed in the same units as the expected value. For the dynamic decision process, the Volatility as a measure for risk includes the time period over which the standard deviation is computed. The Volatility measure is defined as standard deviation divided by the square root of the time duration. What should you do if the course of action with the larger expected outcome also has a much higher risk? In such cases, using another measure of risk known as the Coefficient of Variation is appropriate. Coefficient of Variation CV option the relative risk, with respect to the expected value, which is defined as: Coefficient of Variation CV is the absolute relative deviation with respect to size provided is not zero, expressed in percentage: The coefficient of variation demonstrates the relationship between standard deviation and expected value, by expressing the risk as a percentage of the non-zero expected value. The quality of your decision may be computed by using Measuring Risk. The following table shows the risk measurements computed for the Investment Decision Example: Risk Assessment G 0. Clearly, deposits are risk free. Now, the final question is: Given all this relevant information, what action do you take? It is all up to you. The following table shows the risk measurements computed for the Investment Decision under pure uncertainty i. Again, the final question is: Ranking Process for Preference among Alternatives: Referring to the Bonds and Stocks alternatives in our numerical example, we notice that based in mean-variance, the Bonds alternative Dominates the Stocks alternative. However this is not always the case. For example, consider two independent investment alternatives: Investment I and Investment II with the characteristics outlined in the following table: Revising the Expected Value and the Variance.
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4 thoughts on “How do you write a put option 5 decision making”
Tuesday 4 March 2014, 1:51 am Sir, I am a qualified kinder garden teacher in Srilanka, I am living in saudi since last two years, and I hope to work in a school from this may as my son reaches 2.6 years and ready for playgroup.
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Charles Darwin and Herbert Spencer on the Origin of Species and Principles of Biology (Illustrated).
Tuesday 4 March 2014, 1:51 am Sir, I am a qualified kinder garden teacher in Srilanka, I am living in saudi since last two years, and I hope to work in a school from this may as my son reaches 2.6 years and ready for playgroup.
In order to illustrate this argument, it is crucial to take a deeper look at the structural issues posed by the various microcredit programmes.
More Reading on the Problem of Homelessness - How you can help and how the problem could be solved Learn ways to help the homeless and more solutions to the problem of homelessness in the midst of great wealth.