Before revision: 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.
After revision: This paper investigates an equilibrium feedback control for time-inconsistent objectives. Under a general framework embracing 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.