A mathematical procedure for selecting among alternative utility functions

Gerrit Paul Van Der Schoot
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
more » ... isk 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.
doi:10.14288/1.0094984 fatcat:ekwi6gwqyzbcpg5abf6h2rcfv4