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

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  • Feng, Zixin
  • Tian, Dejian
  • Zheng, Harry

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.

Suggested Citation

  • Feng, Zixin & Tian, Dejian & Zheng, Harry, 2026. "Consumption–investment optimization with Epstein–Zin utility in unbounded non-Markovian markets," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002492
    DOI: 10.1016/j.spa.2025.104805
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