### 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 language | English |
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Pages (from-to) | 301-314 |

Number of pages | 14 |

Journal | Insurance: Mathematics and Economics |

Volume | 93 |

Early online date | 2 Jun 2020 |

DOIs | |

Publication status | Published - 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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## Cite this

Fahrenwaldt, M. A., & Sun, C. (2020). Expected utility approximation and portfolio optimisation.

*Insurance: Mathematics and Economics*,*93*, 301-314. https://doi.org/10.1016/j.insmatheco.2020.05.010