Connections between a system of forward–backward SDEs and backward stochastic PDEs related to the utility maximization problem

Abstract

Connections between a system of Forward–Backward SDEs derived in Horst et al., (2014) and Backward Stochastic PDEs (Mania and Tevzadze, 2010) related to the utility maximization problem are established. Besides, we derive another version of Forward–Backward SDE of the same problem and prove the existence of solution.