- Authors:
- DOI:
- 10.1007/s00780-014-0234-y
- Abstract:
- We develop a theory for a general class of discrete-time stochastic control problems that, in various ways, are time-inconsistent in the sense that they do not admit a Bellman optimality principle. We attack these problems by viewing them within a game theoretic framework, and we look for subgame perfect Nash equilibrium points. For a general controlled Markov process and a fairly general objective functional, we derive an extension of the standard 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. Most known examples of time-inconsistent stochastic control problems in the literature are easily seen to be special cases of the present theory. We also prove that for every time-inconsistent problem, there exists an associated time-consistent problem such that the optimal control and the optimal value function for the consistent problem coincide with the equilibrium control and value function, respectively for the time-inconsistent problem. To exemplify the theory, we study some concrete examples, such as hyperbolic discounting and mean–variance control.
- Type:
- Journal article
- Language:
- English
- Published in:
- Finance and Stochastics, 2014, Vol 18, Issue 3, p. 545-592
- Keywords:
- Time consistency; Time inconsistency; Time-inconsistent control; Dynamic programming; Stochastic control; Bellman equation; Hyperbolic discounting; Mean–variance; Mean-variance; GROWTH
- Main Research Area:
- Social science
- Publication Status:
- Published
- Review type:
- Peer Review
- Submission year:
- 2014
- Scientific Level:
- Scientific
- ID:
- 269206738
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