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Does Markov-Modulation Increase the Risk?

Author

Listed:
  • Asmussen, Søren
  • Frey, Andreas
  • Rolski, Tomasz
  • Schmidt, Volker

Abstract

In this paper we compare ruin functions for two risk processes with respect to stochastic ordering, stop-loss ordering and ordering of adjustment coefficients. The risk processes are as follows: in the Markov-modulated environment and the associated averaged compound Poisson model. In the latter case the arrival rate is obtained by averaging over time the arrival rate in the Markov modulated model and the distribution of the claim size is obtained by averaging the ones over consecutive claim sizes.

Suggested Citation

  • Asmussen, Søren & Frey, Andreas & Rolski, Tomasz & Schmidt, Volker, 1995. "Does Markov-Modulation Increase the Risk?," ASTIN Bulletin, Cambridge University Press, vol. 25(1), pages 49-66, May.
    • Handle: RePEc:cup:astinb:v:25:y:1995:i:01:p:49-66_00
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    Citations

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    Cited by:

    1. Søren Asmussen & Colm O'cinneide, 2002. "On the Tail of the Waiting Time in a Markov-Modulated M/G/1 Queue," Operations Research, INFORMS, vol. 50(3), pages 559-565, June.
    2. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    3. Schmidli, Hanspeter, 2001. "Distribution of the first ladder height of a stationary risk process perturbed by [alpha]-stable Lévy motion," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 13-20, February.
    4. Stanford, David A. & Stroinski, Krzysztof J. & Lee, Karen, 2000. "Ruin probabilities based at claim instants for some non-Poisson claim processes," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 251-267, May.
    5. Nicole Bäuerle & Anja Blatter & Alfred Müller, 2008. "Dependence properties and comparison results for Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 161-186, February.
    6. Asmussen, Søren & Schmidt, Volker, 1995. "Ladder height distributions with marks," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 105-119, July.
    7. Lu, Yi & Li, Shuanming, 2005. "On the probability of ruin in a Markov-modulated risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 522-532, December.
    8. Sotomayor, Luz R. & Cadenillas, Abel, 2011. "Classical and singular stochastic control for the optimal dividend policy when there is regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 344-354, May.
    9. Bauerle, Nicole, 1996. "Some results about the expected ruin time in Markov-modulated risk models," Insurance: Mathematics and Economics, Elsevier, vol. 18(2), pages 119-127, July.

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