Estimating utility functions using generalized maximum entropy

Abstract

This paper estimates von Neumann and Morgenstern utility functions using the generalized maximum entropy (GME), applied to data obtained by utility elicitation methods. Given the statistical advantages of this approach, we provide a comparison of the performance of the GME estimator with ordinary least square (OLS) in a real data small sample setup. The results confirm the ones obtained for small samples through Monte Carlo simulations. The difference between the two estimators is small and it decreases as the width of the parameter support vector increases. Moreover, the GME estimator is more precise than the OLS one. Overall, the results suggest that GME is an interesting alternative to OLS in the estimation of utility functions when data are generated by utility elicitation methods.

Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory

“…The papers by Abbas [4][5][6] where it seems to have been applied for the first time, and later on Abbas (2006), Darooneh [7], Pires et al [8] and Pires et al [9], describe different maxentropic approaches to the problems and contain references to previous work on the specific applications to utility theory. Actually, the transformation of problems (1) into (2) was considered in Abbas' papers.…”

“…Thus, we might decide to consider the problem analyzed in Section 2, that is to reconstruct the second derivative of the utility function by means of the method of maximum entropy in the mean described in Section 4.3. Accordingly, we have to solve (9), where the vector m that is specified right below that equation to be used as input for the numerical analysis is given Table 4. Recall that the procedure of maximum entropy in the mean is used now to determine the second derivative of the utility function, from which the function itself is determined by simple integration.…”