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


  • 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.

Suggested Citation

  • Calvo-Garrido, Maria del Carmen & Pascucci, Andrea & Vázquez Cendón, Carlos, 2012. "Mathematical analysis and numerical methods for pricing pension plans allowing early retirement," MPRA Paper 36494, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:36494

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    References listed on IDEAS

    1. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
    2. E. Chevalier, 2006. "Optimal Early Retirement Near the Expiration of a Pension Plan," Finance and Stochastics, Springer, vol. 10(2), pages 204-221, April.
    3. Bodie, Zvi, 1990. "Pensions as Retirement Income Insurance," Journal of Economic Literature, American Economic Association, vol. 28(1), pages 28-49, March.
    4. Laura Monti & Andrea Pascucci, 2009. "Obstacle problem for Arithmetic Asian options," Papers 0910.4257,
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    More about this item


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

    JEL classification:

    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G00 - Financial Economics - - General - - - General

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