Diffusion limits for a Markov modulated binomial counting process

Peter Spreij; Jaap Storm

doi:10.1017/s0269964818000578

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arXiv · 1801.03682

Diffusion limits for a Markov modulated binomial counting process

Peter Spreij·Jaap Storm

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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.

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Peter Spreij, Jaap Storm. 2018-01-11. Diffusion limits for a Markov modulated binomial counting process. https://doi.org/10.1017/s0269964818000578

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