optimal credit portfolio and consumption with regime switching and default contagion

We study optimal portfolio and consumption in a regime-switching multi-name credit market with default contagion. Defaults generate portfolio losses and alter the intensities of surviving securities. Under Cobb--Douglas utility, homogeneity reduces the HJB equation to a recursive ODE system indexed by the default states. Solving it backward from the all-default state, we establish existence and uniqueness of positive classical solutions, characterize the optimal feedback controls, and prove a verification theorem.