Efficient valuation of guaranteed minimum maturity benefits in regime switching jump diffusion models with surrender risk
The paper deals with an actuarial version of the American option pricing problem. The goal is to price a contract which can be terminated at time \(\tau\), \( \tau \in (0,T]\), with a payoff \[ F_\tau + P(\tau) (G_\tau - F_\tau)^+, \] where \(P(t)\) is an increasing penalty function \[ 0 < P(t) \leq P(T)=1, \] \(G_t\) is a deterministic guaranteed minimum payoff and \(F_t\) is the account value at time \(t\). The provided model is based on the assumption that \(F_t=e^{-ct} S_t\), where \(S_t\) is a regime-switching jump diffusion process such that \(e^{-rt}S_t\) is a martingale in the pricing measure \(Q\) and that the intensity of the stopping time \(\tau\) is a diffusion process.
scientific article; zbMATH DE number 7630795
scientific article