Risk-neutral valuation of GLWB riders in variable annuities

In this paper we propose a model for pricing GLWB variable annuities under 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. The contract value is defined through an optimization problem which is solved by using dynamic programming. We prove, by backward induction, the validity of the bang-bang condition for the set of discrete withdrawal strategies of the model. This result is particularly remarkable as in the insurance literature either the existence of optimal bang-bang controls is assumed or it requires suitable conditions. We assume constant interest rates, although our results still hold in the case of a Markovian interest rate process. We present extensive numerical examples, modelling the mortality intensity as a non mean reverting square root process and the asset price as an exponential Levy process, and compare the results obtained for different parameters and policyholder behaviours.

Automated summary

In this paper, a model is proposed for pricing GLWB variable annuities under a stochastic mortality framework. The contract value is defined through an optimization problem solved by using dynamic programming. The authors prove the validity of the bang-bang condition for the withdrawal strategies of the model using backward induction. Extensive numerical examples are presented, comparing the results for different parameters and policyholder behaviours.