Two-sided Poisson control of linear diffusions
Optimization and Control
2022-07-19 v2 Probability
Abstract
We study a class of two-sided optimal control problems of general linear diffusions under a so-called Poisson constraint: the controlling is only allowed at the arrival times of an independent Poisson signal processes. We give a weak and easily verifiable set of sufficient conditions under which we derive a quasi-explicit unique solution to the problem in terms of the minimal r-excessive mappings of the diffusion. We also investigate limiting properties of the solutions with respect to the signal intensity of the Poisson process. Lastly, we illustrate our results with an explicit example.
Cite
@article{arxiv.2203.09573,
title = {Two-sided Poisson control of linear diffusions},
author = {Harto Saarinen},
journal= {arXiv preprint arXiv:2203.09573},
year = {2022}
}
Comments
23 pages, 2 figures