This paper studies the finite time risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. The Markovian regime-switching process is assumed to be unobservable, which has countable states that affect default intensities of surviving assets. The stochastic control problem is formulated under partial observations of asset prices and default events. By proving an innovative martingale representation theorem based on incomplete and phasing out filtration, we characterize the value function in an equivalent but simplified form. This allows us to connect the previous control problem to a quadratic BSDE with jumps that is new to the literature, in which the driver term has non-standard structures and carries the conditional filter as an infinite-dimensional parameter. By proposing some novel truncation techniques, we obtain the existence of solution to this new BSDE using the delicate convergence of solutions associated to some truncated BSDEs. The verification theorem and the characterization of the optimal trading strategy can be concluded with the aid of our newly established BSDE results.
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