A defaultable financial market with complete information

We consider a Markov-modulated defaultable Brownian market and price the defaultable contingent claims with the intensity-based methodology using the fair price concept under the benchmark approach. We also derive the locally risk-minimizing hedging strategy for defaultable contingent claims under the benchmark approach. We assume that the default intensity and the stock price parameters are modulated by a Markov process. The recovery processes are assumed to have random payments at default time as well as at the maturity of the claims.