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Time-inconsistency with rough volatility

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  • Bingyan Han
  • Hoi Ying Wong

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.

Suggested Citation

  • Bingyan Han & Hoi Ying Wong, 2019. "Time-inconsistency with rough volatility," Papers 1907.11378, arXiv.org, revised Dec 2021.
    • Handle: RePEc:arx:papers:1907.11378
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    References listed on IDEAS

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