Fair valuation of participating policies with surrender options and regime switching

We consider the fair valuation of a participating life insurance policy with surrender options when the market values of the asset are modelled by Markov-modulated Geometric Brownian Motion (GBM). We reduce the dimension of the optimal stopping problem for the policy by changing probability measures. We also provide a decomposition result for the value of the policy. The Barone–Adesi–Whaley approximation has been employed to approximate the solution of the free boundary problem for the policy by second-order piecewise linear ordinary differential equations (ODEs). The fair valuation of participating perpetual American contracts are also considered.