Optimal investment and consumption under $g$- expected utility and general constraints in incomplete market

Paper: arXiv 2501.17193

Authors: Wahid Faidi

Abstract

This article studies the problem of utility maximization in an incomplete market under a class of nonlinear expectations and general constraints on trading strategies. Using a $g$-martingale method, we provide an explicit solution to our optimization problem for different utility functions and characterize an optimal investment-consumption strategy through the solutions to quadratic BSDEs.

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 for portfolio optimization under g-expected utility and general constraints using quadratic BSDEs and g-martingales. However, it is entirely theoretical with zero empirical validation, backtesting, or code provided.

Research Flowchart

  flowchart TD
    A[Goal: Optimal Investment & Consumption<br>under g-Expectations & Constraints] --> B[Inputs: Multi-Asset Incomplete Market,<br>Utility Functions & Strategy Constraints]
    B --> C[Method: Apply g-Martingale Technique<br>to Nonlinear Utility Maximization]
    C --> D[Computation: Solve Associated<br>Quadratic BSDEs]
    D --> E[Outcome: Explicit Optimal Investment-<br>Consumption Strategy Characterization]