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

Listed author(s):
  • Avner Friedman


    (University of Minnesota, Department of Mathematics, Minneapolis, MN 55455, USA)

  • Weixi Shen


    (Department of Mathematics, Fudan University, Shanghai 200433, China Manuscript)

Registered author(s):

    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.

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    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 6 (2002)
    Issue (Month): 3 ()
    Pages: 273-302

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    Handle: RePEc:spr:finsto:v:6:y:2002:i:3:p:273-302
    Note: received: January 2001; final version received: August 2001
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