Mathematical analysis and numerical methods for pricing pension plans allowing early retirement (Q2873873)

This paper deals with mathematical analysis and numerical methods for pricing pension plans allowing for an early retirement. The authors propose a mathematical model to obtain the value of a defined benefit pension plan including early retirement option for the employee. It is assumed that the amount received by the employee depends on the average salary corresponding to a certain number of years before retirement. The considered problem is decomposed into two time regions: one corresponding to the time range to average the salary, and the other being previous to the initial averaging time. For the first time region the authors prove the existence of a solution and analyze its regularity. In the second time region a classical one factor Black-Scholes equation is posed involving a nonhomogeneous term. The authors propose appropriate numerical methods based on a Lagrange-Galerkin discretization and an augmented Lagrangian active set method. Some examples are presented to illustrate the performance of the proposed numerical method as well as the behavior of the solution and the optimal retirement boundary.