This paper is concerned with the determination of credit risk premia of
defaultable contingent claims by means of indifference valuation principles.
Assuming exponential utility preferences we derive representations of
indifference premia of credit risk in terms of solutions of Backward Stochastic
Differential Equations (BSDE). The class of BSDEs needed for that
representation allows for quadratic growth generators and jumps at random
times. Since the existence and uniqueness theory for this class of BSDEs has
not yet been developed to the required generality, the first part of the paper
is devoted to fill that gap. By using a simple constructive algorithm, and
known results on continuous quadratic BSDEs, we provide sufficient conditions
for the existence and uniqueness of quadratic BSDEs with discontinuities at
random times
