# Characterization of Fully Coupled FBSDE in Terms of Portfolio Optimization

## TL;DR

This paper characterizes fully coupled FBSDEs through BSDE sub-solutions, applying it to utility optimization under uncertainty, and provides explicit examples for pricing and recursive utilities.

## Contribution

It offers a new verification and characterization framework for coupled FBSDEs and demonstrates their application in utility and pricing problems.

## Key findings

- Explicit methods to quantify costs of market incompleteness
- Procedures to find optimal solutions for recursive utilities
- Application of FBSDE characterization to utility optimization

## Abstract

We provide a verification and characterization result of optimal maximal sub-solutions of BSDEs in terms of fully coupled forward backward stochastic differential equations. We illustrate the application thereof in utility optimization with random endowment under probability and discounting uncertainty. We show with explicit examples how to quantify the costs of incompleteness when using utility indifference pricing, as well as a way to find optimal solutions for recursive utilities.