Valuation of Complex Life Insurance Products under Regime-Switching Jump Diffussion Models

This paper introduces a valuation framework for complex life insurance products with guaranteed benefits, utilizing a hybrid financial market model with regime-switching jump diffusion processes as risk drivers. The model accounts for the interplay between financial and surrender risks, providing explicit analytical formulas. These formulas are computed using both continuous-time Markov chains (CTMC) and the Fourier cosine series (COS) expansion method. The paper also outlines effcient numerical procedures for practical implementation.