Resumé
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Finance and Stochastics |
| Vol/bind | 18 |
| Udgave nummer | 3 |
| Sider (fra-til) | 545-592 |
| ISSN | 0949-2984 |
| DOI | |
| Status | Udgivet - 2014 |
Emneord
- Time consistency
- Time inconsistency
- Time-inconsistent control
- Dynamic programming
- Stochastic control
- Bellman equation
- Hyperbolic discounting
- Mean–variance
Citer dette
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A Theory of Markovian Time-inconsistent Stochastic Control in Discrete Time. / Björk, Tomas; Murgoci, Agatha.
I: Finance and Stochastics, Bind 18, Nr. 3, 2014, s. 545-592.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review
TY - JOUR
T1 - A Theory of Markovian Time-inconsistent Stochastic Control in Discrete Time
AU - Björk, Tomas
AU - Murgoci, Agatha
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Time consistency
KW - Time inconsistency
KW - Time-inconsistent control
KW - Dynamic programming
KW - Stochastic control
KW - Bellman equation
KW - Hyperbolic discounting
KW - Mean–variance
U2 - 10.1007/s00780-014-0234-y
DO - 10.1007/s00780-014-0234-y
M3 - Journal article
VL - 18
SP - 545
EP - 592
JO - Finance and Stochastics
JF - Finance and Stochastics
SN - 0949-2984
IS - 3
ER -