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Local risk minimization for vulnerable European contingent claims on nontradable assets under regime switching models. (English) Zbl 1344.49031
Summary: This article focuses on an optimal hedging problem of the vulnerable European contingent claims. The underlying asset of the vulnerable European contingent claims is assumed to be nontradable. The interest rate, the appreciation rate and the volatility of risky assets are modulated by a finite-state continuous-time Markov chain. By using the local risk minimization method, we obtain an explicit closed-form solution for the optimal hedging strategies of the vulnerable European contingent claims. Further, we consider a problem of hedging for a vulnerable European call option. Optimal hedging strategies are obtained. Finally, a numerical example for the optimal hedging strategies of the vulnerable European call option in a two-regime case is provided to illustrate the sensitivities of the hedging strategies.

MSC:
49J55 Existence of optimal solutions to problems involving randomness
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J28 Applications of continuous-time Markov processes on discrete state spaces
60J27 Continuous-time Markov processes on discrete state spaces
93E20 Optimal stochastic control
91B30 Risk theory, insurance (MSC2010)
91G80 Financial applications of other theories
65C05 Monte Carlo methods
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