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In this paper, we address the mathematical analysis and numerical solution of a model for pricinga defined benefit pension plan. More precisely, the benefits received by the member of the plandepend on the average salary and early retirement is allowed. Thus, the mathematical model isposed as an obstacle problem associated to a Kolmogorov equation in the time region where thesalary is being averaged. Previously to the initial averaging date, a nonhomogeneous one factorBlack-Scholes equation is posed. After stating the model, existence and regularity of solutionsare studied. Moreover, appropriate numerical methods based on a Lagrange-Galerkin discretizationand an augmented Lagrangian active set method are proposed. Finally, some numerical examplesillustrate the performance of the numerical techniques and the properties of the solution and thefree boundary.

Mathematical Analysis and Numerical Methods for Pricing Pension Plans Allowing Early Retirement