Dynamic programming for multidimensional stochastic control problems |
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| Authors: | Jin Ma Jiongmin Yong |
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| Affiliation: | (1) Department of Mathematics, Purdue University, 47907-1395 West Lafayette, IN, USA;(2) Laboratory of Mathematics for Nonlinear Science, Department of Mathematics, and Institute of Mathematical Finance, Fudan University, 200433 Shanghai, P. R. China |
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| Abstract: | 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. Supported in part by USA Office of Naval Research grant #N00014-96-1-0262. Supported in part by the NSFC Grant #79790130, the National Distinguished Youth Science Foundation of China Grant #19725106 and the Chinese Education Ministry Science Foundation. |
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| Keywords: | Stochastic control Dynamic programming Viscosity solutions Singular control Impulse control |
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