Dynamic Withdrawals and Stochastic Mortality in GLWB Variable Annuities

In this paper we propose a discrete time model, based on dynamic programming, to price GLWB variable annuities under the dynamic approach within a stochastic mortality framework. Our set-up is very general and only requires the Markovian property for the mortality intensity and the asset price processes. We also show the validity of the bang-bang condition for the set of discrete withdrawal strategies of the model. This result allows to drastically reduce the computational time needed to search the optimal withdrawal in the backward recursive step of our dynamic algorithm and provides, as a by-product, an interesting contract decomposition.