Utility maximization with random horizon: a BSDE approach

TL;DR

This paper addresses utility maximization with a random horizon by analyzing a novel BSDE with singular coefficients, establishing existence and uniqueness, and demonstrating results through numerical simulations.

Contribution

It introduces a new class of BSDEs with singular coefficients for utility maximization with random horizons, proving their well-posedness.

Findings

Existence and uniqueness of solutions for the BSDE with singular coefficients.

Numerical simulations illustrating the theoretical results.

Abstract

In this paper we study a utility maximization problem with random horizon and reduce it to the analysis of a specific BSDE, which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by numerical simulations.