A locally risk minimizing hedging strategy under a regime switching Lévy model.

*(Chinese. English summary)*Zbl 1299.91129Summary: In this paper, we suppose that the risky asset follows a Markov-modulated geometric Lévy process, the market interest rate, the appreciation rate and the volatility rate of the risky asset, and the intensity and magnitude of the jump depend on the states of the economy which are described by a continuous-time Markov chain. Since the market which we considered is incomplete, we find an optimal hedging strategy for an European contingent claim by employing the local risk minimization method. Then we also provide an example and obtain the numerical result of an optimal risk hedging strategy for an European call option under a Markov-modulated geometry Brownian motion. Finally, this optimal risk hedging strategy and the Delta hedging strategy under the Black-Scholes model are compared in this paper, and we prove that the uncertain factors of Markov chain will bring the impact on the investment decision of risk manager.