Mathematical analysis and numerical methods for pricing pension plans allowing early retirement
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.
|Date of creation:||06 Feb 2012|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- E. Chevalier, 2006. "Optimal Early Retirement Near the Expiration of a Pension Plan," Finance and Stochastics, Springer, vol. 10(2), pages 204-221, April.
- Bodie, Zvi, 1990.
"Pensions as Retirement Income Insurance,"
Journal of Economic Literature,
American Economic Association, vol. 28(1), pages 28-49, March.
- Zvi Bodie, 1989. "Pensions as Retirement Income Insurance," NBER Working Papers 2917, National Bureau of Economic Research, Inc.
- Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
- Andrea, Pascucci, 2007. "Free boundary and optimal stopping problems for American Asian options," MPRA Paper 4766, University Library of Munich, Germany.
- Laura Monti & Andrea Pascucci, 2009. "Obstacle problem for Arithmetic Asian options," Papers 0910.4257, arXiv.org. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:36494. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.