A variational inequality approach to financial valuation of retirement benefits based on salary
type: Item
instance of: scholarly article
title: A variational inequality approach to financial valuation of retirement benefits based on salary
zbMATH Open document ID: 1029.91027
author: A. Friedman
author: Weixi Shen
published in: Finance and Stochastics
publication date: 2003-10-22T00:00:00Z
review text: A pension plan is considered with the option of early retirement. I.e. the paid benefits \(\Psi(s,t)\) based on the salary \(S\) and the time of retirement \(t\) is defined as \(\Psi(S,T)=V(S,T)\), where \(T\) is the end period and \(V\) is the financial value of the retirement benefits. If \(T_0<t<T\), then \( \Psi(S(t),t)=(1-(T-t)/(T-T_0))\max(A_0,a(t)S(t)), \) where \(A_0\) is a predefined amount independent of the contributions made by the member, \(a(t)\) is a positive valued function. If \(t<T_0\), then \(\Psi(S(t),t)=0\). \(S\) is supposed to be a diffusion process. A variational inequality is derived for \(V\) and it is shown that \(V\) is the unique solution of it. The set of points \((S,T)\), where the retiring member receive the full value of the retirement consists of one or two continuous curves.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 1995765
zbMATH Keywords: free boundary
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: optimal time
MaRDI profile type: Publication
full work available at URL: s007800100059
OpenAlex ID: W2032972744
DOI: 10.1007/S007800100059
description: scientific article; zbMATH DE number 1995765