Geodesic
Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization
Kybernetika, Tome 54 (2018) no. 6, pp. 1167-1183.

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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.
DOI : 10.14736/kyb-2018-6-1167
Classification : 34E05, 35K55, 70H20, 90C15, 91B16, 91B70
Keywords: dynamic stochastic portfolio optimization; Hamilton-Jacobi-Bellman equation; Conditional value-at-risk; $CVaRD$-based Sharpe ratio 
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     title = {Expected utility maximization and conditional value-at-risk deviation-based {Sharpe} ratio in dynamic stochastic portfolio optimization},
     journal = {Kybernetika},
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Kilianová, Soňa; Ševčovič, Daniel. Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization. Kybernetika, Tome 54 (2018) no. 6, pp. 1167-1183. doi : 10.14736/kyb-2018-6-1167. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-6-1167/

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