Polynomial Utility

Abstract

We approximate the utility function by polynomial series and solve the related dynamic portfolio optimization problems. We study the quality of the approximation for the Taylor and Bernstein series in response to the center and the degree of the expansion. The issue of time-inconsistency, arising from a dynamically adapted center of the expansion, is approached by equilibrium theory. In the numerical study we focus on two specific utility functions: For power utility, access to the optimal portfolio allows for a more complete illustration of the approximations; for the S-shaped utility function of prospect theory, the use of equilibrium theory allows for approximating the solution to the (obviously interesting but yet unsolved) case of current wealth as a dynamic reference point.

Keywords: Dynamic programming, Optimal Asset Allocation, Expected Utility Theory, Polynomial Expansions