Pricing pension plans under jump–diffusion models for the salary

In this paper we consider the valuation of a defined benefit pension plan in the presence of jumps in the underlying salary and including the possibility of early retirement. We will consider that the salary follows a jump–diffusion model, thus giving rise to a partial integro-differential equation (PIDE). After posing the model, we propose the appropriate numerical methods to solve the PIDE problem. These methods mainly consists of Lagrange–Galerkin discretizations combined with augmented Lagrangian active set techniques and with the explicit treatment of the integral term. Finally, we compare the numerical results with those ones obtained with Monte Carlo techniques.