CalvoGarrido, Maria del Carmen and Pascucci, Andrea and Vázquez Cendón, Carlos (2012): Mathematical analysis and numerical methods for pricing pension plans allowing early retirement.

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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 BlackScholes equation is posed. After stating the model, existence and regularity of solutions are studied. Moreover, appropriate numerical methods based on a LagrangeGalerkin 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.
Item Type:  MPRA Paper 

Original Title:  Mathematical analysis and numerical methods for pricing pension plans allowing early retirement 
English Title:  Mathematical analysis and numerical methods for pricing pension plans allowing early retirement 
Language:  English 
Keywords:  retirement plans, options pricing, Kolmogorov equations, complementarity problem, numerical methods, augmented Lagrangian formulation 
Subjects:  G  Financial Economics > G2  Financial Institutions and Services > G23  Nonbank Financial Institutions; Financial Instruments; Institutional Investors G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing; Futures Pricing G  Financial Economics > G0  General > G00  General 
Item ID:  36494 
Depositing User:  Andrea Pascucci 
Date Deposited:  07. Feb 2012 15:04 
Last Modified:  12. Feb 2013 00:30 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/36494 