Pricing and managing risks of ruin contingent life annuities under regime switching variance gamma process

We propose a model for valuing ruin contingent life annuities under the regime-switching variance gamma process. The Esscher transform is employed to determine the equivalent martingale measure. The PIDE approach is adopted for the pricing formulation. Due to the path dependency of the payoff of the insurance product and the non-existence of a closed-form solution for the PIDE, the finite difference method is utilized to numerically calculate the value of the product. To highlight some practical features of the product, we present a numerical example. Finally, we examine numerically the performance of a simple hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as the value at risk and the expected shortfall. The impacts of the frequency of re-balancing the hedging portfolio on the quality of hedging are also discussed.