Polynomial Utility

30 Pages Posted: 5 Jan 2022

See all articles by Alexander Sevel Lollike

Alexander Sevel Lollike

University of Copenhagen; University of Copenhagen

Mogens Steffensen

University of Copenhagen

Date Written: Oktober 10, 2021

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

Suggested Citation

Lollike, Alexander Sevel and Steffensen, Mogens, Polynomial Utility (Oktober 10, 2021). Available at SSRN: https://ssrn.com/abstract=3999066 or http://dx.doi.org/10.2139/ssrn.3999066

Alexander Sevel Lollike (Contact Author)

University of Copenhagen ( email )

Nørregade 10
Copenhagen, København DK-1165
Denmark

University of Copenhagen ( email )

Nørregade 10
Copenhagen, København DK-1165
Denmark

Mogens Steffensen

University of Copenhagen ( email )

Universitetsparken 5
DK-2100 Copenhagen
Denmark

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