Analysis and computation of an optimality equation arising in an impulse control problem with discrete and costly observations

2020 ◽  
Vol 366 ◽  
pp. 112399 ◽  
Author(s):  
Hidekazu Yoshioka ◽  
Motoh Tsujimura
2012 ◽  
Vol 450-451 ◽  
pp. 46-55
Author(s):  
Shao Lin Tian ◽  
Ji Chun Li ◽  
Kun Hui Liu

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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