  This paper investigates the finite horizon risk-sensitive portfolio
optimization in a regime-switching credit market with physical and
information-induced default contagion. It is assumed that the underlying
regime-switching process has countable states and is unobservable. The
stochastic control problem is formulated under partial observations of asset
prices and sequential default events. By establishing a martingale
representation theorem based on incomplete and phasing out filtration, we
connect the control problem to a quadratic BSDE with jumps, in which the driver
term is non-standard and carries the conditional filter as an
infinite-dimensional parameter. By proposing some truncation techniques and
proving a uniform a priori estimates, we obtain the existence of a solution to
the BSDE using the convergence of solutions associated to some truncated BSDEs.
The verification theorem can be concluded with the aid of our BSDE results,
which in turn yields the uniqueness of the solution to the BSDE.
