Diffusion limits for a Markov modulated binomial counting process
Probability
2020-03-25 v2
Abstract
In this paper we study limit behavior for a Markov-modulated (MM) binomial counting process, also called a binomial counting process under regime switching. Such a process naturally appears in the context of credit risk when multiple obligors are present. Markov-modulation takes place when the failure/default rate of each individual obligor depends on an underlying Markov chain. The limit behavior under consideration occurs when the number of obligors increases unboundedly, and/or by accelerating the modulating Markov process, called rapid switching. We establish diffusion approximations, obtained by application of (semi)martingale central limit theorems. Depending on the specific circumstances, different approximations are found.
Cite
@article{arxiv.1801.03682,
title = {Diffusion limits for a Markov modulated binomial counting process},
author = {Peter Spreij and Jaap Storm},
journal= {arXiv preprint arXiv:1801.03682},
year = {2020}
}