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

Soňa Kilianová; Daniel Ševčovič

Kybernetika (2018)

  • Volume: 54, Issue: 6, page 1167-1183
  • ISSN: 0023-5954

Abstract

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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 ( C V a R D ) 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 C V a R D -based Sharpe ratio on the utility function and the associated risk aversion level.

How to cite

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Kilianová, Soňa, and Ševčovič, Daniel. "Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization." Kybernetika 54.6 (2018): 1167-1183. <http://eudml.org/doc/294336>.

@article{Kilianová2018,
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.},
author = {Kilianová, Soňa, Ševčovič, Daniel},
journal = {Kybernetika},
keywords = {dynamic stochastic portfolio optimization; Hamilton-Jacobi-Bellman equation; Conditional value-at-risk; $CVaRD$-based Sharpe ratio},
language = {eng},
number = {6},
pages = {1167-1183},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization},
url = {http://eudml.org/doc/294336},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Kilianová, Soňa
AU - Ševčovič, Daniel
TI - Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 6
SP - 1167
EP - 1183
AB - 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.
LA - eng
KW - dynamic stochastic portfolio optimization; Hamilton-Jacobi-Bellman equation; Conditional value-at-risk; $CVaRD$-based Sharpe ratio
UR - http://eudml.org/doc/294336
ER -

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