Expected utility approximation and portfolio optimisation

Matthias A. Fahrenwaldt, Chaofan Sun

Research output: Contribution to journalArticle

Abstract

Classical portfolio selection problems that optimise expected utility can usually not be solved in closed form. It is natural to approximate the utility function, and we investigate the accuracy of this approximation when using Taylor polynomials. In the important case of a Merton market and power utility we show analytically that increasing the order of the polynomial does not necessarily improve the approximation of the expected utility. The proofs use methods from the theory of parabolic second-order partial differential equations. All results are illustrated by numerical examples.

Original languageEnglish
Pages (from-to)301-314
Number of pages14
JournalInsurance: Mathematics and Economics
Volume93
Early online date2 Jun 2020
DOIs
Publication statusPublished - Jul 2020

Keywords

  • Asymptotic analysis
  • Expected utility
  • Mean–variance optimisation
  • Portfolio selection
  • Power utility

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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