Martingale representation and admissible portfolio process with regime switching

We discuss the existence of an admissible investment strategy for any given consumption rate process in a Markov, regime-switching Black-Scholes-Merton economy. A martingale representation for a double martingale generated by the Brownian motion and the Markov chain is used to establish the existence of the admissible investment strategy. We also employ the martingale representation to prove the attainability of a European contingent claim in the regime-switching environment under a pricing kernel specified by the Esscher transform based on the Laplace cumulant process.