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

TL;DR

This paper introduces a novel randomization approach to develop robust forward investment and consumption strategies that account for drift and volatility uncertainties in incomplete markets, ensuring optimality and robustness.

Contribution

It proposes a new method using endogenous randomization to construct robust forward preferences and strategies under non-zero volatility and model uncertainty.

Findings

Constructed robust randomized forward preferences.

Derived optimal investment and consumption strategies.

Validated strategies remain optimal in the physical market.

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.