Terminal wealth problem under uncertainty: how to choose the right asset mix in case of dependent random payments

We develop an approximate solution method for a classical saving for retirement problem in case of random payment scheme and value at risk (VaR) defined investor preferences. As the results of our numerical calculations indicate our approximate approach provides greater accuracy and reduces simulation time required for computing certain risk measures. One should note that our approximate approach is in no way restrictive and applies only to VaR defined preferences; our approximating sequence adequately describes the distribution function of terminal wealth, thus also making solutions accurate in case of utility defined preferences.