Dynamic programming for multidimensional stochastic control problems

Authors
Ma, J Yong, J
Citation
J. Ma et J. Yong, Dynamic programming for multidimensional stochastic control problems, ACTA MATH S, 15(4), 1999, pp. 485-506
Citations number
20
Categorie Soggetti
Mathematics
Journal title
ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN journal
10009574 → ACNP
Volume
15
Issue
4
Year of publication
1999
Pages
485 - 506
Database
ISI
SICI code
1000-9574(199910)15:4<485:DPFMSC>2.0.ZU;2-Y
Abstract
In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem, sin gular 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-variationa l inequality is proved.