A regular equilibrium solves the extended HJB system

Abstract

Control problems not admitting the dynamic programming principle are known as time-inconsistent. The game-theoretic approach is to interpret such problems as intrapersonal dynamic games and look for subgame perfect Nash equilibria. A fundamental result of time-inconsistent stochastic control is a verification theorem saying that solving the extended HJB system is a sufficient condition for equilibrium. We show that solving the extended HJB system is a necessary condition for equilibrium, under regularity assumptions. The controlled process is a general Itô diffusion.

References in corpus (3)

• Being serious about non-commitment: subgame perfect equilibrium in continuous time
• On time-inconsistent stopping problems and mixed strategy stopping times
• On Finding Equilibrium Stopping Times for Time-Inconsistent Markovian Problems

Cited by in corpus (4)

• On time-inconsistent stopping problems and mixed strategy stopping times
• Nonlocality, Nonlinearity, and Time Inconsistency in Stochastic Differential Games
• Time-Consistent Asset Allocation for Risk Measures in a Lévy Market
• A PDE approach for open-loop equilibriums in time-inconsistent stochastic optimal control problems