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# week9da - Spring 2010 DecisionAnalysis MS405 Risk and...

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Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring Spring , 2010 , 2010 Decision Analysis   MS 405    Risk and Utility Kemal Kılıç Faculty of Engineering and Natural Sciences Week 8 1

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Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring Spring , 2010 , 2010 Risk - Introduction \$14.50 Game 1 Game 2 0.5 0.5 0.5 0.5 Payoff \$30 - \$1 \$2,000 - \$1,900 \$50.00 Figure 13.1 Which one would you prefer to play? Week 8 2
Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring Spring , 2010 , 2010 Utility Functions Assuming a lottery(game) f with a set of states S and a set of prizes X , a utility function is any function u : X x S -> R (that is, into the real numbers) Note: The utility of a monetary prize of \$X, u(\$X), is not necessarily equal or proportional to |X|, especially when X is a significant portion of the decision maker’s net worth When X is sufficiently small relative to the current wealth, it is reasonable to assume a linear utility function of the money Week 8 3

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Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring Spring , 2010 , 2010 Attitudes Toward Risk An individual’s utility function is a mathematical function that transforms monetary values - payoffs and costs - into utility values . Most researchers believe that if certain basic behavioral assumptions hold, people are expected utility maximizers - that is, they choose the alternative with the largest expected utility. (Not always – think about framing!) Week 8 4
Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring Spring , 2010 , 2010 Attitudes Toward Risk Week 8 5

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Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring Spring , 2010 , 2010 Attitudes Toward Risk An individual’s utility function is a mathematical function that transforms monetary values - payoffs and costs - into utility values . Most researchers believe that if certain basic behavioral assumptions hold, people are expected utility maximizers - that is, they choose the alternative with the largest expected utility. (Not always – think about framing!) Essentially an individual’s utility function specifies the individual’s preferences for various monetary payoffs and costs and, in doing so, it automatically encodes the individual’s attitudes toward risk. Week 8 6
Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring Spring , 2010 , 2010 Attitudes Toward Risk -- continued Most individuals are risk averse , which means intuitively that they are willing to sacrifice some EMV to avoid risky gambles. Utility functions for monetary values (wealth) are said to be increasing and concave. This means they go uphill and they increase at a decreasing rate.

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week9da - Spring 2010 DecisionAnalysis MS405 Risk and...

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