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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 450-451A Class of Stochastic Control Problem Governed by...

A Class of Stochastic Control Problem Governed by a Poisson Process

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Abstract:

In this paper, we examine an optimal impulse control problem of stochastic system, whose state follows a Brownian motion. Here we want to maximum the objective function. The main feature of our model is that the controlled state process includes an impulse control governed by a Poisson process. In other words, the set of possible intervention times are discrete, random and determined by the signal process. Here we not only present a theorem giving a sufficient condition on the existence of an optimal control and its corresponding objective function, but also provide an explicit solution obtained under some simplified conditions.

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Periodical:

Advanced Materials Research (Volumes 450-451)

Pages:

46-55

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.450-451.46

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Online since:

January 2012

Authors:

Shao Lin Tian, Ji Chun Li, Kun Hui Liu

Keywords:

Generalized Ito Formula, Impulse Contro, Optimal Stopping, Poisson Process, Variational Inequality

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© 2012 Trans Tech Publications Ltd. All Rights Reserved

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