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Lundberg-type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin under a Markov-modulated Risk Model

  • Andrew C.Y. Ng (a1) and Hailiang Yang (a1)
Abstract

In this paper, we consider a Markov-modulated risk model (also called Markovian regime switching insurance risk model). Follow Asmussen (2000, 2003), by using the theory of Markov additive process, an exponential martingale is constructed and Lundberg-type upper bounds for the joint distribution of surplus immediately before and at ruin are obtained. As a natural corollary, bounds for the distribution of the deficit at ruin are obtained. We also present some numerical results to illustrate the tightness of the bound obtained in this paper.

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References
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Asmussen, S. (1989) “Risk theory in a Markovian environment’’. Scandinavian Actuarial Journal, 1989, 69100.
Asmussen, S. (2000) Ruin Probabilities. World Scientific.
Asmussen, S. (2003) Applied Probability and Queues. 2nd ed., New York: Springer-Verlag.
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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
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