Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach

ArXiv ID: 2410.01378 “View on arXiv”

Authors: Unknown

Abstract

This paper studies robust forward investment and consumption preferences and optimal strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with drift and volatility uncertainties. We focus on non-zero volatility and constant relative risk aversion forward preferences. Given the non-convexity of the Hamiltonian with respect to uncertain volatilities, we first construct robust randomized forward preferences through endogenous randomization in an auxiliary market. {“Therein, w”}e derive the corresponding optimal and robust investment and consumption strategies. Furthermore, we show that such forward preferences and strategies, developed in the auxiliary market, remain optimal and robust in the physical market, offering a comprehensive {“analysis”} for forward investment and consumption under model uncertainty.

Keywords: model uncertainty, forward preferences, Hamiltonian, incomplete market, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats
• Why: The paper is highly mathematically advanced, relying on backward stochastic differential equations (BSDEs), fully nonlinear SPDEs, randomization techniques, and saddle-point analysis to address drift and volatility uncertainty. It is purely theoretical, focusing on existence proofs and optimality characterizations without any empirical data, backtesting, or implementation details.

  flowchart TD
    A["Research Goal: Find robust forward investment and consumption strategies under drift and volatility uncertainties in incomplete markets"] --> B{"Key Challenge"}
    B --> C["Hamiltonian non-convexity w.r.t uncertain volatilities"]
    C --> D["Methodology: Construct robust randomized forward preferences"]
    D --> E["Derive optimal strategies in auxiliary market"]
    E --> F["Prove strategy optimality & robustness in physical market"]
    F --> G["Key Outcomes"]
    G --> H["Robust investment and consumption strategies under model uncertainty"]
    G --> I["Comprehensive analysis for forward preferences in incomplete markets"]