Probabilistic Analysis Lecture Slides

Probabilistic Analysis Lecture Slides - Risk(Probabilistic...

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Risk (Probabilistic Analysis) Risk (Probabilistic Analysis) IE 430, Fall 2014, Instructor: Yu-Ching Lee November 11, 2014 1 / 90
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Risk (Probabilistic Analysis) A. Basic Concepts of Uncertainty i. Terminology ii. The distribution of Random Variables B. Evaluation of Projects with Random Variable i. Evaluation of Projects with Discrete Random Variable ii. Evaluation of Projects with Continuous Random Variable C. Evaluation of Risk and Uncertainty by Monte Carlo Simulation D. Decision Trees E. Real Options Analysis 2 / 90
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Risk (Probabilistic Analysis) A. Basic Concepts of Uncertainty i. Terminology Degree of Confidence In previous topics, it was assumed that a high degree of confidence could be placed in all estimated values including revenues, costs, and other quantities. The degree of confidence is sometimes called assumed certainty . Decisions made solely on the basis of this kind of analysis are sometimes called decisions under certainty . 3 / 90
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Risk (Probabilistic Analysis) A. Basic Concepts of Uncertainty i. Terminology Decision under Risk v.s. Decision under Uncertainty The motivation for dealing with risk and uncertainty is to establish the bounds of error such that another alternative being considered may turn out to be a better choice than the one we recommended under assumed certainty. Decisions under risk are decisions in which the analyst models the decision problem in terms of assumed possible future outcomes, or scenarios, whose probabilities of occurrence can be estimated. A decision under uncertainty , by contrast, is a decision problem characterized by several unknown futures for which probabilities of occurrence cannot be estimated. 4 / 90
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Risk (Probabilistic Analysis) A. Basic Concepts of Uncertainty i. Terminology Random Variables A cost, revenue, useful life, equivalent-worth, or rate-of-return value for a cash-flow all can be a factor having probabilistic outcomes, which is called a random variable . The expected value and variance of random variable are used to make the uncertainty associated with each alternative more explicit, including any probability of loss. Thus, when uncertainty is considered, the variability in the economic measures of merit and the probability of loss associated with the alternatives are normally used in the decision-making process. 5 / 90
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Risk (Probabilistic Analysis) A. Basic Concepts of Uncertainty ii. The distribution of Random Variables Probability Mass Function and Cumulative Distribution Function Capital letters such as X , Y , and Z are usually used to represent random variables and lowercase letters ( x , y , z ) to denote the particular values that these variables take on in the sample space. When a random variable’s sample space is discrete, its probability mass function is usually indicated by p ( x ) and its cumulative distribution function by P ( x ).
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