A Theory of Markovian Time Inconsistent Stochastic Control in Continuous Time

44 Pages Posted: 4 Feb 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: February 2, 2016

Abstract

In this paper, which is a continuation of the discrete time paper, we develop a theory for 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. Within the framework of a controlled SDE 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. As applications of the general theory we study non exponential discounting as well as 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, stochastic control, Bellman equation, hyperbolic discounting, mean-variance, equilibrium

JEL Classification: C61, C72, C73, G11

Suggested Citation

Bjork, Tomas and Khapko, Mariana and Murgoci, Agatha, A Theory of Markovian Time Inconsistent Stochastic Control in Continuous Time (February 2, 2016). Available at SSRN: https://ssrn.com/abstract=2727480 or http://dx.doi.org/10.2139/ssrn.2727480

Tomas Bjork

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 (Contact Author)

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

Nordre Ringgade 1
Aarhus C, DK-8000
Denmark

Register to save articles to
your library

Register

Paper statistics

Downloads
162
Abstract Views
615
rank
182,177
PlumX Metrics