On time-inconsistent stochastic control in continuous time

In this paper, which is a continuation of the discrete-time paper (Björk 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....

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Vydáno v:Finance and stochastics Ročník 21; číslo 2; s. 331 - 360
Hlavní autoři: Björk, Tomas, Khapko, Mariana, Murgoci, Agatha
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2017
Springer Nature B.V
Témata:
Dynamic programming
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Equilibrium
Finance
Game theory
Inconsistency
Insurance
Management
Markov analysis
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Stochastic models
Studies
Time
Verification
Bellman equation
60J70
G11
Time-inconsistency
G12
Equilibrium
49L99
D5
91A10
Time-consistency
Hyperbolic discounting
Time-inconsistent control
91B02
49N90
91B25
Stochastic control
Dynamic programming
Mean-variance
91A80
91B51
91G80
C73
C61
C72
ISSN:0949-2984, 1432-1122
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Popis
Shrnutí:In this paper, which is a continuation of the discrete-time paper (Björk 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 ).
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-017-0327-5