  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.
