15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 10 - Angewandte Mathematik, Industrie- und Finanzmathematik
Montag, 17. September 2001, 15.00, Hörsaal 42

 

A Variational Inequality Approach to Financial Valuation of Retirement Benefits

Avner Friedman, University of Minnesota (Koautor: Weixi Chen)

 

The Black-Schole model for American put option allows one to compute the value of an option by solving a parabolic variational inequality. The corresponding free boundary tells one when the best time is to sell the option. In this talk we describe an analogous approach to the problem of early retirement. We consider a pension plan with the option of early retirement. The paid benefits $_\Psi(S,t)$ are the larger of two quantities:(i) a guaranteed sum A, (ii) a multiple of the salary $S(t)$ at the time of retirement. The financial value of the retirement plan, $V=V(S,t)$ then satisfies a variational inequality, which is derived by combining ideas from actuarial mathematics with the stochastic nature of $S(t)$. We determine the curve $V(S,t)=_\Psi(S,t)$, which is the optimal time for early retirement (from a financial point of view) and, in particular, study its asymptotic behavior near the end-period $t=T$ of the pension plan.

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