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In this paper we investigate the expected terminal utility maximizationapproach for a dynamic stochastic portfolio optimization problem. We solve itnumerically by solving an evolutionary Hamilton-Jacobi-Bellman equation whichis transformed by means of the Riccati transformation. We examine thedependence of the results on the shape of a chosen utility function in regardto the associated risk aversion level. We define the  Conditional value-at-risk deviation ($CVaRD$) based Sharpe ratio formeasuring risk-adjusted performance of a dynamic portfolio. We compute optimalstrategies for a portfolio investment problem motivated by the German DAX 30Index and we evaluate and analyze the dependence of the $CVaRD$-based Sharperatio on the utility function and the associated risk aversion level.

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