This paper investigates an equilibrium feedback control for time-inconsistent reward functionals when the state variable follows a Volterra process. As Volterra processes are non-Markovian and non-semimartingale in general , we develop an extended path-dependent Hamilton-Jacobi-Bellman (PHJB) equation system and offer a verification theorem to the solution of the PHJB equation. We apply the theory to three time-inconsistent problemswhen the risky asset price follows the Volterra Heston model, a typical rough volatility model. Analytical solutions are derived for the three problems: mean-variance portfolio problem (MVP) with constant risk aversion, MVP with a state-dependent risk aversion , and an investment/consumption problem with non-exponential discounting . Through these examples, we address the effects of roughness on equilibrium strategies .
Motivated by recent advances in rough volatility, this paper investigates the impact of roughness on equilibrium feedback strategies for time-inconsistent objectives. Under a general framework embracing non-Markovian and non-semimartingale models , we develop an extended path-dependent Hamilton-Jacobi-Bellman (PHJB) equation system . A verification theorem is provided. By deriving explicit solutions to three problems, including mean-variance portfolio problem (MVP) with constant risk aversion, MVP for log-returns , and an investment/consumption problem with non-exponential discounting , we present that volatility roughness adjusts the equilibrium strategies considerably, up to 40\% in certain settings. Since rough volatility models capture the near-term downside risk by fitting the volatility skews, we interpret the adjustments as a hedge for this risk .
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This paper investigates an equilibrium feedback control
Motivated by recent advances in rough volatility, this paper investigates the impact of roughness on equilibrium feedback strategies
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reward functionals when the state variable follows a Volterra process. As Volterra processes are
objectives. Under a general framework embracing
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in general
models
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and offer a verification theorem to the solution of the PHJB equation. We apply the theory to three time-inconsistent problemswhen the risky asset price follows the Volterra Heston model, a typical rough volatility model. Analytical solutions are derived for the three problems:
. A verification theorem is provided. By deriving explicit solutions to three problems, including
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with a state-dependent risk aversion
for log-returns
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. Through these examples, we address the effects of roughness on equilibrium strategies
, we present that volatility roughness adjusts the equilibrium strategies considerably, up to 40\% in certain settings. Since rough volatility models capture the near-term downside risk by fitting the volatility skews, we interpret the adjustments as a hedge for this risk