Article
MSC:
34E05,
35K55,
70H20,
90C15,
91B16,
91B70 | MR 3902627 | Zbl 07031767 | DOI: 10.14736/kyb-2018-6-1167
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Keywords:
dynamic stochastic portfolio optimization; Hamilton-Jacobi-Bellman equation; Conditional value-at-risk; $CVaRD$-based Sharpe ratio
dynamic stochastic portfolio optimization; Hamilton-Jacobi-Bellman equation; Conditional value-at-risk; $CVaRD$-based Sharpe ratio
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.
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