TY - JOUR

T1 - Polynomial Utility

AU - Lollike, Alexander S.

AU - Steffensen, Mogens

N1 - Publisher Copyright: ©c World Scientific Publishing Company.

PY - 2023

Y1 - 2023

N2 - We approximate the utility function by polynomial series and solve the related dynamic portfolio optimization problems. We study the quality of the Taylor and Bernstein series approximation in response to the points and degrees of the expansions and generalize from earlier expansions applied to portfolio optimization. The issue of time inconsistency, arising from a dynamically adapted center of the expansion, is approached by equilibrium theory. We present new ways of constructing polynomial utility functions and study their pitfalls and potentials. In the numerical study, we focus on two specific utility functions: For power utility, access to the optimal portfolio allows for a 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.

AB - We approximate the utility function by polynomial series and solve the related dynamic portfolio optimization problems. We study the quality of the Taylor and Bernstein series approximation in response to the points and degrees of the expansions and generalize from earlier expansions applied to portfolio optimization. The issue of time inconsistency, arising from a dynamically adapted center of the expansion, is approached by equilibrium theory. We present new ways of constructing polynomial utility functions and study their pitfalls and potentials. In the numerical study, we focus on two specific utility functions: For power utility, access to the optimal portfolio allows for a 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.

KW - Dynamic programming

KW - expected utility theory

KW - optimal asset allocation

KW - polynomial expansions

U2 - 10.1142/S0219024923500243

DO - 10.1142/S0219024923500243

M3 - Journal article

AN - SCOPUS:85181453473

VL - 26

JO - International Journal of Theoretical and Applied Finance

JF - International Journal of Theoretical and Applied Finance

SN - 0219-0249

IS - 06n07

M1 - 2350024

ER -