| Type de publication : |
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Articles dans des revues avec comité de lecture |
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| Domaine : |
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| Titre : |
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Time-Inconsistent Stochastic Linear--Quadratic Control |
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| Auteur(s) : |
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Ying Hu ( ) 1, Hanqing Jin, Xun Yu Zhou |
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| Laboratoire : |
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| Équipe de recherche : |
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Processus stochastiques |
| Résumé : |
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In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we find an explicit equilibrium control. As an application, we then consider a mean-variance portfolio selection model in a complete financial market where the risk-free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes. Applying the general sufficient condition, we obtain explicit equilibrium strategies when the risk premium is both deterministic and stochastic. |
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Langue du texte
intégral : |
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Anglais |
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Date de production,
écriture : |
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03/11/2011 |
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| Journal : |
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| SIAM Journal on Control and Optimization |
| Publisher |
Society for Industrial and Applied Mathematics |
| ISSN |
0363-0129 |
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| Audience : |
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internationale |
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| Date de publication : |
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2012 |
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| Volume : |
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50 |
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| Numéro : |
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3 |
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| Page, identifiant, ... : |
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1548-1572 |
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| Mots Clés : |
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time-inconsistency – stochastic linear-quadratic control – equilibriumcontrol – forward-backward stochastic differential equation – mean-variance portfolio selection |
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| Classification : |
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93E99, 60H10, 91B28 |
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