Robust optimal investment and consumption strategies with portfolio constraints and stochastic environment

TL;DR

This paper develops a comprehensive framework for optimal investment and consumption under model uncertainty, incorporating constraints and ambiguity aversion, and analyzes their effects through advanced stochastic control methods and numerical experiments.

Contribution

It introduces a robust control approach for constrained investment-consumption problems with model uncertainty, linking ambiguity aversion to optimal strategies and welfare loss.

Findings

Short-selling restrictions reduce utility loss under model uncertainty.

Consumption constraints' impact depends on risk aversion level.

Numerical results show significant effects of ambiguity aversion and constraints.

Abstract

We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to robustness captured by the homothetic multiplier robust specification, and the investor's investment and consumption strategies are constrained to closed convex sets. To solve this constrained robust control problem, we employ the stochastic Hamilton-Jacobi-Bellman-Isaacs equations, backward stochastic differential equations, and bounded mean oscillation martingale theory. Furthermore, we show the investor incurs (non-negative) utility loss, i.e. the loss in welfare, if model uncertainty is ignored. When the model coefficients are deterministic, we establish formally the relationship between the investor's robustness preference and the robust optimal investment-consumption strategy and the value function, and the impact of investment and consumption constraints on the investor's robust optimal investment-consumption strategy and value function. Extensive numerical experiments highlight the significant impact of ambiguity aversion, consumption and investment constraints, on the investor's robust optimal investment-consumption strategy, utility loss, and value function. Key findings include: 1) short-selling restriction always reduces the investor's utility loss when model uncertainty is ignored; 2) the effect of consumption constraints on utility loss is more delicate and relies on the investor's risk aversion level.