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

Keywords

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

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