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Expected Utility Maximization and Conditional Value-at-Risk Deviation-based Sharpe Ratio in Dynamic Stochastic Portfolio Optimization

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  • Sona Kilianova
  • Daniel Sevcovic

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.

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  • Sona Kilianova & Daniel Sevcovic, 2018. "Expected Utility Maximization and Conditional Value-at-Risk Deviation-based Sharpe Ratio in Dynamic Stochastic Portfolio Optimization," Papers 1810.11619, arXiv.org.
    • Handle: RePEc:arx:papers:1810.11619
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    File URL: http://arxiv.org/pdf/1810.11619
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    Cited by:

    1. Pedro Polvora & Daniel Sevcovic, 2021. "Utility indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation," Papers 2108.12598, arXiv.org.
    2. Daniel Sevcovic & Cyril Izuchukwu Udeani, 2023. "Hamilton-Jacobi-Bellman Equation Arising from Optimal Portfolio Selection Problem," Papers 2308.02627, arXiv.org.
    3. Jose Cruz & Maria Grossinho & Daniel Sevcovic & Cyril Izuchukwu Udeani, 2022. "Linear and Nonlinear Partial Integro-Differential Equations arising from Finance," Papers 2207.11568, arXiv.org.

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