Before revision:  We also consider the optimal measure transformation problem for defaultable bonds, futures contracts, and forward contracts. We provide financial interpretations of the optimal measure transformation problems in terms of the  maximization of returns subject to a relative entropy penalty term.
After revision:  We also consider the optimal measure is characterized using a semimartingale BSDE under general conditions. The EMT is used to reinterpret the conditional entropic risk-measure and to obtain a convenient formula for the conditional expectation of a process which admits an affine representation under a related measure. The entropic measure transform is then used provide a new characterization of defaultable bond prices, forward prices, and futures prices when the asset is driven by a jump diffusion. The characterization of these pricing problems in terms of the maximization of returns subject to a relative entropy penalty term.