Robust portfolio selection with uncertain exit time using worst-case VaR strategy

In this paper we consider the robust portfolio selection problem involving two types of uncertainties; the uncertainty in the distribution of exit time and the uncertainty in the distribution of portfolio return conditional on exit time. To deal with these uncertainties, we propose a tractable approach by applying worst-case VaR strategy to the case where partial information on the exit time distribution and on the conditional distribution of portfolio return is available, and formulate the corresponding problems as semidefinite programs which can be efficiently solved. Moreover, we present some numerical results with real market data.