A variational inequality approach to financial valuation of retirement benefits based on salary
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.
scientific article; zbMATH DE number 1995765