Ruin probabilities for a risk model with two classes of claims

Tong Ling Lv, Jun Yi Guo, Xin Zhang

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process. We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in infinite time horizon is obtained.

Original languageEnglish
Pages (from-to)1749-1760
Number of pages12
JournalActa Mathematica Sinica, English Series
Volume26
Issue number9
DOIs
Publication statusPublished - 2010

Keywords

  • exponential martingale
  • infinitesimal generator
  • Markov vector process
  • piecewise-deterministic Markov process (PDMP)
  • ruin probability

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