Pricing pension plans based on average salary without early retirement:partial differential equation modeling and numerical solution

摘要

In this paper, a partial differential equation model for the pricing of pension plans based on average salary is posed by using the dynamic hedging methodology. The existence and uniqueness of solutions for the resulting initial-value problem associated with a Kolmogorov equation is obtained. Moreover, a numerical method based on a Crank-Nicolson characteristics time discretization combined with finite elements to approximate the solution is proposed. Finally, some test examples illustrate the performance of the numerical methods as a tool for pricing these pension plans.