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

Avner Friedman () and Weixi Shen ()
Additional contact information
Avner Friedman: University of Minnesota, Department of Mathematics, Minneapolis, MN 55455, USA
Weixi Shen: Department of Mathematics, Fudan University, Shanghai 200433, China Manuscript

Finance and Stochastics, 2002, vol. 6, issue 3, 273-302

Abstract: We consider a pension plan with the option of early retirement, and paid benefits $\Psi (S,t)$ based on salary S at the time of retirement, but with guaranteed minimum; $S=S(t)$ is a Markov process. Denote by V(S,t) the financial value of the retirement benefits; its formal definition is given in (1.16). Then $\Psi (S,t) = V(S,t)$ at the end period T, while $\Psi (S,t)\leq V(S,t)$ if early retirement is exercised. We prove that V is the unique solution of a variational inequality, and that the set $\{\Psi = V\}$, which corresponds to the optimal time to retire, consists of either one or two continuous curves $S = S_i(t)$, depending on the parameters of the model.

Keywords: Retirement benefits; variational inequality; free boundary; stochastic differential equations; optimal time (search for similar items in EconPapers)
JEL-codes: G23 (search for similar items in EconPapers)
Date: 2002-05-17
Note: received: January 2001; final version received: August 2001
References: Add references at CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://link.springer.de/link/service/journals/00780/papers/2006003/20060273.pdf (application/pdf)
Access to the full text of the articles in this series is restricted

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:6:y:2002:i:3:p:273-302

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().