Time-inconsistency with rough volatility
Abstract
In this paper, we consider equilibrium strategies under Volterra processes and time-inconsistent preferences embracing mean-variance portfolio selection (MVP). Using a functional It\^o calculus approach, we overcome the non-Markovian and non-semimartingale difficulty in Volterra processes. The equilibrium strategy is then characterized by an extended path-dependent Hamilton-Jacobi-Bellman equation system under a game-theoretic framework. A verification theorem is provided. We derive explicit solutions to three problems, including MVP with constant risk aversion, MVP for log returns, and a mean-variance objective with a linear controlled Volterra process. We also thoroughly examine the effect of volatility roughness on equilibrium strategies. Numerical experiments demonstrate that trading rules with rough volatility outperform the classic counterparts.
Keywords
Cite
@article{arxiv.1907.11378,
title = {Time-inconsistency with rough volatility},
author = {Bingyan Han and Hoi Ying Wong},
journal= {arXiv preprint arXiv:1907.11378},
year = {2021}
}
Comments
An earlier version of this paper was circulated and cited under the title "Time-consistent feedback strategies with Volterra processes"