Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets

TL;DR

This paper develops a method to determine optimal consumption and investment strategies for investors with Epstein-Zin utility in complex, unbounded, non-Markovian markets using advanced stochastic calculus techniques.

Contribution

It introduces a novel approach employing quadratic BSDEs with exponential moments to solve the consumption-investment problem in non-Markovian, unbounded market settings.

Findings

Derived explicit optimal strategies using quadratic BSDEs.

Extended the dual problem analysis to complex market models.

Demonstrated the applicability of the method in realistic financial scenarios.

Abstract

The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial scenarios compared to the Markovian setting. The optimal consumption and investment strategies are derived using the martingale optimal principle and quadratic backward stochastic differential equations (BSDEs) whose solutions admit some exponential moment. This integrability property plays a crucial role in establishing a key martingale argument. In addition, the paper also examines the associated dual problem and several models within the specified parameter framework.