Department of Economics and Business Economics

On time-inconsistent stochastic control in continuous time

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  • Tomas Bjork, Stockholm School of Economics
  • ,
  • Mariana Khapko, University of Toronto, St. Michael's Hospital, Toronto
  • ,
  • Agatha Murgoci

In this paper, which is a continuation of the discrete-time paper (Bjork and Murgoci in Finance Stoch. 18:545-592, 2004), 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 nonlinear equations, for the determination of 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 (Cox et al. in Econometrica 53:363-384, 1985).

Original languageEnglish
JournalFinance and Stochastics
Pages (from-to)331-360
Number of pages30
Publication statusPublished - Apr 2017

    Research areas

  • Time-consistency, Time-inconsistency, Time-inconsistent control, Dynamic programming, Stochastic control, Bellman equation, Hyperbolic discounting, Mean-variance, Equilibrium, MODEL

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