DIFFUSION LIMITS FOR A MARKOV MODULATED BINOMIAL COUNTING PROCESS

Peter Spreij, P.J. Storm

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this paper, we study limit behavior for a Markov-modulated 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.
Original languageEnglish
Number of pages23
JournalProbability in the Engineering and Informational Sciences
DOIs
Publication statusPublished - 30 Jan 2019

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Diffusion Limit
Counting Process
Limit Behavior
Markov processes
Martingale Central Limit Theorem
Regime Switching
Credit Risk
Diffusion Approximation
Semimartingale
Markov Process
Markov chain
Modulation
Approximation
Counting process
Context
Regime switching
Markov process
Diffusion approximation
Default rate
Central limit theorem

Keywords

  • Markov-modulated process
  • central limit theorems
  • counting process
  • functional limit theorems

Cite this

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DIFFUSION LIMITS FOR A MARKOV MODULATED BINOMIAL COUNTING PROCESS. / Spreij, Peter; Storm, P.J.

In: Probability in the Engineering and Informational Sciences, 30.01.2019.

Research output: Contribution to JournalArticleAcademicpeer-review

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