Numerical solutions of quantile hedging for guaranteed minimum death benefits under a regime-switching jump-diffusion formulation
This paper considers hedging problems containing both financial and insurance risk and perfect hedging is impossible because of the mortality risk, and the incompleteness of the market, due to regime switching. In the proposed model, the rate of return and the volatility, and the insurance charge, are modulated by a finite-state Markov chain, which represents the market modes and other economic conditions. To find the optimal hedging strategies, it is needed to solve a system of Hamilton-Jacobi-Bellman (HJB) integro-differential equations. Using Markov chain approximation techniques, a discrete-time controlled Markov chain with two components is constructed. Under simple conditions, the convergence of the approximation to the value function is established. Examples of quantile hedging for guaranteed minimum death benefits are also presented..
scientific article; zbMATH DE number 5863181