Optimal Early Retirement Near the Expiration of a Pension Plan
Tóm tắt
In a recent paper, Friedman and Shen (Finance Stoch 6: 273–302, 2002) have considered a pension plan with the option of early retirement. They showed that the financial value V of the retirement benefits is the solution of a variational inequality and have studied the associated free boundary. A description of the free boundary near maturity is given, thanks to integral equation methods. However, V is also the solution of an optimal stopping problem very close to the American option valuation problem. Comparing V to specific options, we derive an expansion of the free boundary near the expiration of the pension plan.
Tài liệu tham khảo
Chevalier E. (2005) Critical price near maturity for an American option on a dividend-paying stock in a local volatility model. Math Finance 15, 439–463
Friedman A., Shen W. (2002) A variational inequality approach to financial valuation of retirement benefits based on salary. Finance Stoch 6, 273–302
Lamberton D. (2002) Brownian optimal stopping and random walks. Appl Math Optim 45, 283–324
Lamberton D., Villeneuve S. (2003) Critical price for an American option on dividend-paying stock. Ann Appl Probab 13, 800–815
Myneni R. (1992) The pricing of the American option. Ann Appl Probab 2, 1–23
Sherris M. (1993) Contingent claims valuation of “Greater of” benefits. Actuar Res Clearing House 1, 87–105
Sherris M. (1995) The valuation of option feature in retirement benefits. J Risk Insur 62, 509–535
Sherris, M., Shen, W. Financial valuation of retirement benefits based on salary. In: Quantitative Methods in Finance 1999 conference, Sydney (1999)
Van Moerbeke P. (1976) On optimal stopping and free boundary problems. Arch Ration Mech Anal 20, 101–148