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

**Authors:** Wing Fung Chong, Gechun Liang  
**arXiv:** [2410.01378](https://arxiv.org/abs/2410.01378)  
**Date:** 2024-10-02  
**Summary page:** https://www.summarizepaper.com/en/paper/2410.01378v1/

## Key points

- Authors Wing Fung Chong and Gechun Liang focus on robust forward investment and consumption preferences in an incomplete financial market.
- Study addresses uncertainties in both drift and volatility for a risk-averse and ambiguity-averse agent.
- Research emphasizes non-zero volatility and constant relative risk aversion (CRRA) forward preferences.
- Introduction of robust randomized forward preferences through endogenous randomization within an auxiliary market to address non-convexity of the Hamiltonian concerning uncertain volatilities.
- Derivation of optimal and robust investment as well as consumption strategies catering to the agent's risk aversion tendencies.
- Notable contribution: Forward preferences and strategies developed in the auxiliary market maintain optimality and robustness when applied to the physical market.
- Research offers innovative approaches for managing risks associated with drift and volatility uncertainties in financial markets, providing insights for future studies.

## Summary

In their paper titled "Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach," authors Wing Fung Chong and Gechun Liang delve into the realm of robust forward investment and consumption preferences in an incomplete financial market. The study focuses on the optimal strategies for a risk-averse and ambiguity-averse agent facing uncertainties in both drift and volatility. Specifically, the research hones in on non-zero volatility and constant relative risk aversion (CRRA) forward preferences. The crux of the paper lies in addressing the non-convexity of the Hamiltonian concerning uncertain volatilities. To tackle this challenge, Chong and Liang introduce a novel concept of constructing robust randomized forward preferences through endogenous randomization within an auxiliary market. By doing so, they are able to derive optimal and robust investment as well as consumption strategies that cater to the agent's risk aversion tendencies. One notable contribution of this study is the demonstration that these forward preferences and strategies developed in the auxiliary market maintain their optimality and robustness when applied to the physical market. This finding underscores the comprehensive framework presented by Chong and Liang, offering valuable insights into navigating forward investment and consumption decisions amidst model uncertainty. Overall, this research sheds light on innovative approaches to managing risks associated with drift and volatility uncertainties in financial markets, providing a solid foundation for future studies in this domain.