Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets
Mathematical Finance
2025-10-27 v2
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.
Keywords
Cite
@article{arxiv.2407.19995,
title = {Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets},
author = {Zixin Feng and Dejian Tian and Harry Zheng},
journal= {arXiv preprint arXiv:2407.19995},
year = {2025}
}
Comments
29 pages