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Kybernetika 54 no. 6, 1167-1183, 2018

Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization

Soňa Kilianová and Daniel ŠevčovičDOI: 10.14736/kyb-2018-6-1167

Abstract:

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation ($CVaRD$) based Sharpe ratio for measuring risk-adjusted performance of a dynamic portfolio. We compute optimal strategies for a portfolio investment problem motivated by the German DAX 30 Index and we evaluate and analyze the dependence of the $CVaRD$-based Sharpe ratio on the utility function and the associated risk aversion level.

Keywords:

Hamilton-Jacobi-Bellman equation, dynamic stochastic portfolio optimization, Conditional value-at-risk, $CVaRD$-based Sharpe ratio

Classification:

35K55, 34E05, 70H20, 91B70, 90C15, 91B16

paper.pdf

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