MATHEMATICAL ANALYSIS AND NUMERICAL METHODS FOR PRICING PENSION PLANS ALLOWING EARLY RETIREMENT

作者：Carmen Calvo Garrido M; Pascucci Andrea; Vazquez Carlos^*

来源：SIAM Journal on Applied Mathematics, 2013, 73(5): 1747-1767.

DOI：10.1137/120864751

• retirement plans
• options pricing
• Kolmogorov equations
• complementarity problem
• numerical methods
• augmented Lagrangian formulation

In this paper, we address the mathematical analysis and numerical solution of a model for pricing a defined benefit pension plan. More precisely, the benefits received by the member of the plan depend on the average salary and early retirement is allowed. Thus, we formulate the mathematical model in terms of an obstacle problem associated to a Kolmogorov equation in the time region where the salary is being averaged. Previously to the initial averaging date, we pose a nonhomogeneous one factor Black-Scholes equation. After stating the model, we study the existence and regularity of solutions. Moreover, we propose appropriate numerical methods based on a Lagrange-Galerkin discretization and an augmented Lagrangian active set method. Finally, some numerical examples illustrate the performance of the numerical techniques and the properties of the solution and the free boundary.

• 出版日期2013