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Option Pricing and Hedging for Regime-Switching Geometric Brownian Motion Models

We propose an equivalent martingale measure for the regime-switching geometric Brownian motion, together with a hedging formula. It is shown that this choice is optimal in the sense that it minimizes the quadratic mean between the payoff at maturity and the value of the hedging portfolio, under the objective measure. The solution is easy to implement since Monte Carlo simulations can be used to obtain the option value as well as the optimal hedging strategy. Two examples of application are considered.