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


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


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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36494.

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Date of creation: 06 Feb 2012
Date of revision:
Handle: RePEc:pra:mprapa:36494

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Related research

Keywords: retirement plans; options pricing; Kolmogorov equations; complementarity problem; numerical methods; augmented Lagrangian formulation;

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  1. Andrea, Pascucci, 2007. "Free boundary and optimal stopping problems for American Asian options," MPRA Paper 4766, University Library of Munich, Germany.
  2. Laura Monti & Andrea Pascucci, 2009. "Obstacle problem for Arithmetic Asian options," Papers 0910.4257,
  3. Zvi Bodie, 1989. "Pensions as Retirement Income Insurance," NBER Working Papers 2917, National Bureau of Economic Research, Inc.
  4. E. Chevalier, 2006. "Optimal Early Retirement Near the Expiration of a Pension Plan," Finance and Stochastics, Springer, vol. 10(2), pages 204-221, April.
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