On Time Inconsistent Stochastic Control in Continuous Time

32 Pages Posted: 27 Dec 2016

See all articles by Tomas Bjork

Tomas Bjork

Stockholm School of Economics - Swedish House of Finance

Mariana Khapko

University of Toronto - Finance Area; Swedish House of Finance

Agatha Murgoci

Aarhus University - School of Business and Social Sciences

Date Written: December 26, 2016

Abstract

In this paper, which is a continuation of a previously published discrete time paper, we study a class of continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We study these problems within a game theoretic framework, and we look for Nash subgame perfect equilibrium points. For a general controlled continuous time Markov process and a fairly general objective functional we derive an extension of the standard Hamilton-Jacobi-Bellman equation, in the form of a system of non-linear equations, for the determination for the equilibrium strategy as well as the equilibrium value function. The main theoretical result is a verification Theorem. As an application of the general theory we study a time inconsistent linear quadratic regulator. We also present a study of time inconsistency within the framework of a general equilibrium production economy of Cox-Ingersoll-Ross type.

Keywords: Time consistency, time inconsistency, time inconsistent control, dynamic programming

JEL Classification: C61, C72, C73, D5, G11, G12

Suggested Citation

Bjork, Tomas and Khapko, Mariana and Murgoci, Agatha, On Time Inconsistent Stochastic Control in Continuous Time (December 26, 2016). Finance and Stochastics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2890162

Tomas Bjork (Contact Author)

Stockholm School of Economics - Swedish House of Finance ( email )

Drottninggatan 98
111 60 Stockholm
Sweden

Mariana Khapko

University of Toronto - Finance Area ( email )

Toronto, Ontario M5S 3E6
Canada

Swedish House of Finance ( email )

Drottninggatan 98
Stockholm
Sweden

Agatha Murgoci

Aarhus University - School of Business and Social Sciences ( email )

Nordre Ringgade 1
Aarhus C, DK-8000
Denmark

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