NDLI: The generalization of a class of impulse stochastic control models of a geometric Brownian motion

Content Provider	Springer Nature Link
Author	Liu, XiaoPeng Liu, KunHui
Copyright Year	2009
Abstract	Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment. This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process. By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls. Meanwhile, we also analyze the structure of optimal controls carefully. Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent. Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent. In addition, this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses, and makes analyses and discussions of the model have the exactitude of mathematical sense.
Starting Page	983
Ending Page	998
Page Count	16
File Format	PDF
ISSN	10092757
Journal	Science in China Series : Information Sciences
Volume Number	52
Issue Number	6
e-ISSN	18622836
Language	English
Publisher	SP Science in China Press
Publisher Date	2009-06-09
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	impulse stochastic control geometric Brownian motion variational equation optimal control Information Systems and Communication Service
Content Type	Text
Resource Type	Article
Subject	Computer Science

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