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

Maria del Carmen Calvo-Garrido, Andrea Pascucci and Carlos Vázquez Cendón

MPRA Paper from University Library of Munich, Germany

Abstract: 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, the mathematical model is posed as an obstacle problem associated to a Kolmogorov equation in the time region where the salary is being averaged. Previously to the initial averaging date, a nonhomogeneous one factor Black-Scholes equation is posed. After stating the model, existence and regularity of solutions are studied. Moreover, appropriate numerical methods based on a Lagrange-Galerkin discretization and an augmented Lagrangian active set method are proposed. Finally, some numerical examples illustrate the performance of the numerical techniques and the properties of the solution and the free boundary.

Keywords: retirement plans; options pricing; Kolmogorov equations; complementarity problem; numerical methods; augmented Lagrangian formulation (search for similar items in EconPapers)
JEL-codes: G00 G13 G23 (search for similar items in EconPapers)
Date: 2012-02-06
New Economics Papers: this item is included in nep-age and nep-cmp
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