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

2024-10-02

AI Summary

This paper addresses the robust forward investment and consumption problem for risk- and ambiguity-averse investors in incomplete financial markets under joint drift and volatility uncertainty. To overcome the nonconvexity of the Hamiltonian induced by volatility uncertainty—which renders conventional methods inapplicable—we pioneer an endogenous randomization mechanism to construct an auxiliary market, thereby transforming the original problem into a convex optimization and enabling robust migration of forward preferences between the physical and auxiliary markets. Leveraging stochastic control, forward utility theory, and robust control frameworks—combined with CRRA utility modeling—we derive explicit optimal strategies and rigorously establish their robustness in the original market. This work establishes, for the first time, a dynamic portfolio allocation framework for forward preferences that jointly accommodates both drift and volatility uncertainty.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Planning under Uncertainty
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 (CRRA) 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. We 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 framework for forward investment and consumption under model uncertainty.

Problem

• Robust investment and consumption under drift and volatility uncertainties
• Optimal strategies for ambiguity-averse agents in incomplete markets
• Forward preferences construction through endogenous randomization approach

Innovation

• Randomization approach for robust preferences
• Auxiliary market with endogenous randomization
• Optimal strategies under model uncertainty