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Risk minimizing option pricing in a regime switching market. (English) Zbl 1133.91415
Summary: We study option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of a stock depends on a finite state Markov chain. Using a minimal martingale measure we show that the risk minimizing option price satisfies a system of Black-Scholes partial differential equations with weak coupling.

MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
91B70 Stochastic models in economics
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