A regular equilibrium solves the extended HJB system
Optimization and Control
2020-05-04 v6
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 It\^o diffusion.
Cite
@article{arxiv.1611.02902,
title = {A regular equilibrium solves the extended HJB system},
author = {Kristoffer Lindensjö},
journal= {arXiv preprint arXiv:1611.02902},
year = {2020}
}