Before revision: We introduce an optimal measure transformation problem for zero coupon bond prices based on dynamic relative entropy of probability measures. In the default-free case we prove the equivalence of the optimal measure transformation problem and an optimal stochastic control problem of Gombani and Runggaldier (Math. Financ. 23(4):659-686, 2013) for bond prices. We also consider the optimal measure transformation problem for defaultable bonds, futures contracts, and forward contracts.
After revision: We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure transformation problem for defaultable bonds, futures contracts, and forward contracts.