Connections between a system of Forward-Backward SDEs and Backward Stochastic PDEs related to the utility maximization problem

TL;DR

This paper explores the relationship between forward-backward stochastic differential equations and backward stochastic PDEs in the context of utility maximization, introducing a new FBSDE formulation and proving solution existence.

Contribution

It establishes connections between FBSDEs and BSPDEs for utility maximization and presents a new FBSDE version with proven solution existence.

Findings

Established links between FBSDEs and BSPDEs in utility maximization

Derived a new FBSDE formulation for the problem

Proved existence of solutions for the new FBSDE

Abstract

Connections between a system of Forward-Backward SDEs and Backward Stochastic PDEs related to the utility maximiza- tion problem is established. Besides, we derive another version of FBSDE of the same problem and prove an existence of a solution