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Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization. (English) Zbl 1463.91128

Summary: 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.

MSC:

91G10 Portfolio theory
93E20 Optimal stochastic control
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