2Department of Management (UTSc),
Rotman School of Management,
University of Toronto,
105 St. George Street, Toronto, ON,
M5S 3E6, Canada
(email: mariana.khapko@rotman.utoronto.ca)
3Department of Economics and Business Economics,
Aarhus University,
Fuglesangs Allé 4,
8210 Aarhus V,
Denmark
(email: agatha.murgoci@econ.au.dk)
Abstract
In this paper, which is a continuation of the discrete-time paper (Björk/Murgoci; A theory of Markovian time-inconsistent stochastic control in discrete time), 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 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.