Financial/Actuarial Mathematics Seminar

Fall 2004: Thursdays 3:10-4:00, 3088 East Hall



A variational inequality approach to financial valuation of retirement benefits based on salary

Kristen Moore

University of Michigan, Mathematics

March 10, 2005



Abstract

I will present a paper by Avner Friedman and Weixi Shen in which they study the optimal retirement time for a participant in a pension plan that pays the larger of a guaranteed minimum or salary-based benefit. The authors assume that the salary evolves randomly and that the individual is subject to two random decrements: death and termination of employment. Moreover, the benefit is reduced if the individual retires prior to her normal retirement date.

The individual should not retire as long as the value of the retirement benefit exceeds the benefit payout; thus, the problem is reminiscent of an American option pricing problem.

Friedman and Shen present a variational inequality that governs the value of the retirement benefit, prove the existence of a unique solution to the variational inequality, and give a characterization of the free boundary.


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