Dynamic programming for multidimensional stochastic control problems

In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem, singular control problem and impulse control problem as special cases. Using a unified treatment of dynamic programming, we show that the value function...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 15; no. 4; pp. 485 - 506
Main Authors Ma, Jin, Yong, Jiongmin
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.10.1999
Subjects
Decomposition
Diffusion
Dynamic programming
Inequalities
Mathematical analysis
Mathematical models
Mathematics
Optimal control
Stochastic control theory
Stochastic processes
Stochasticity
Studies
Uniqueness
Viscosity
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Summary:In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem, singular control problem and impulse control problem as special cases. Using a unified treatment of dynamic programming, we show that the value function of the problem is a viscosity solution of certain Hamilton-Jacobi-Bellman (HJB) quasivariational inequality. The uniqueness of such a quasi-variational inequality is proved.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-999-0081-5