Before revision:  We contribute to both of these problems by obtaining novel characterizations of option prices and optimal portfolio strategies under regime-switching . Using our option price representation, we develop a novel efficient method to price claims which may depend on the full path of the underlying Markov chain. This is done via a change of probability measure and a short-time asymptotic expansion of the claim's price in terms of the Laplace transforms of the symmetric Dirichlet distribution .
After revision:  We contribute to both of these problems by obtaining novel characterizations of option prices and optimal portfolio strategies under regime-switching market driven by an underlying continuous- time Markov process. As a result of this representation, along with a short-time asymptotic expansion of the claim's price in terms of the Laplace transforms of the symmetric Dirichlet distribution .