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

Paper: arXiv 2407.19995

Authors: Zixin Feng, Dejian Tian, Harry Zheng

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using quadratic BSDEs to solve the Epstein-Zin utility optimization problem in unbounded non-Markovian markets. While mathematically sophisticated and complete in its proofs, it is a purely theoretical work with no empirical backtesting or real-world data application.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve Epstein-Zin Consumption-Investment Problem in Unbounded Non-Markovian Markets] --> B[Inputs: Multi-Asset Incomplete Market & Stochastic Parameters]
    B --> C[Methodology: Martingale Optimal Principle & Stochastic Control]
    C --> D[Formulate Quadratic BSDEs with Exponential Integrability]
    D --> E[Solve Dual Optimization Problem]
    E --> F[Outcomes: Explicit Optimal Consumption & Investment Strategies]