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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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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 
@article{10_14736_kyb_2018_6_1167,
     author = {Kilianov\'a, So\v{n}a and \v{S}ev\v{c}ovi\v{c}, Daniel},
     title = {Expected utility maximization and conditional value-at-risk deviation-based {Sharpe} ratio in dynamic stochastic portfolio optimization},
     journal = {Kybernetika},
     pages = {1167--1183},
     year = {2018},
     volume = {54},
     number = {6},
     doi = {10.14736/kyb-2018-6-1167},
     mrnumber = {3902627},
     zbl = {07031767},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-6-1167/}
}
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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

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