A regular equilibrium solves the extended HJB system

• 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 Ito diffusion. 

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Dynamic inconsistency

Extended HJB system

Subgame perfect Nash equilibrium

Time-inconsistent preferences

Time-inconsistent stochastic control

Publication and Content Type

ref (subject category)

art (subject category)