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UBC Theses and Dissertations

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UBC Theses and Dissertations

A mathematical procedure for selecting among alternative utility functions Schoot, Gerrit Paul van der

Abstract

This thesis presents a mathematical procedure, called the R^-method, for selecting among alternative utility functions to represent a decision maker's risk preference. A general class of utility functions is introduced and for five alternative members of this class, the absolute risk aversion at the initial wealth w[sub o] , i.e. R[sub A](w[sub o] ), is expressed as a function of: (i) the parameters of a nondegenerate gamble z; and (ii) the decision maker's response to that gamble (in terms of risk premium, or certainty equivalent, or probability equivalent, or gain equivalent). Mathematical results are obtained for two different gambles. The R[sub A]-method calculates the values of R[sub A] for several responses to different reference gambles, and then selects the utility function with the least relative standard deviation over the R[sub A] values. The procedure is based on the fact, that for the decision maker's actual utility function, R[sub A] must theoretically attain the same value at w[sub o], namely R[sub A](w[sub o]), no matter what gamble is used to assess R[sub A]. Suggestions are made for extending the R[sub A]-method to incorporate risk proneness as well as attitudes which are risk averse over one part of the domain and risk seeking over another part. Finally, a chapter on mathematical extensions is provided in order to improve the R[sub A]-method by including a larger set of alternative utility functions.

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