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On matrix-exponential distributions in risk theory

Author

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  • Alessandra Carleo
  • Mariafortuna Pietroluongo

Abstract

In this paper, a particular class of matrix-exponential distributions is described, also with respect to its use in risk theory, namely phase-type distributions. Phase-type distributions have the important advantage of being suitable for approximating most of other distributions as well as being mathematically tractable. After a review on phase-type distributions and their properties, a possible use in risk theory is illustrated. Modelling both interarrival claim times and individual claim sizes with this class of distributions an explicit formula for the probability of ultimate ruin is given.

Suggested Citation

  • Alessandra Carleo & Mariafortuna Pietroluongo, 2014. "On matrix-exponential distributions in risk theory," Discussion Papers 2_2014, CRISEI, University of Naples "Parthenope", Italy.
    • Handle: RePEc:crj:dpaper:2_2014
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    File URL: http://www.crisei.uniparthenope.it/wp/materiale/crisei_pietroluongo.pdf
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    References listed on IDEAS

    as
    1. Jang, Jiwook, 2007. "Jump diffusion processes and their applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 62-70, July.
    2. Hipp, Christian, 2006. "Speedy convolution algorithms and Panjer recursions for phase-type distributions," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 176-188, February.
    3. Steve Drekic & Gordon Willmot, 2005. "On the Moments of the Time of Ruin with Applications to Phase-Type Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 17-30.
    4. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    5. Stanford, D.A. & Avram, F. & Badescu, A.L. & Breuer, L. & Silva Soares, A. Da & Latouche, G., 2005. "Phase-type Approximations to Finite-time Ruin Probabilities in the Sparre-Andersen and Stationary Renewal Risk Models," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 131-144, May.
    6. Ahn, Soohan & Badescu, Andrei L., 2007. "On the analysis of the Gerber-Shiu discounted penalty function for risk processes with Markovian arrivals," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 234-249, September.
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    Keywords

    Matrix-exponential distribution; Phase-type distribution; Ruin probability; Markov chain.;
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