IDEAS home Printed from https://ideas.repec.org/p/crj/dpaper/2_2014.html

On matrix-exponential distributions in risk theory

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.crisei.uniparthenope.it/wp/materiale/crisei_pietroluongo.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhimin Zhang & Eric C. K. Cheung, 2016. "The Markov Additive Risk Process Under an Erlangized Dividend Barrier Strategy," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 275-306, June.
    2. Yang Li & Yaolei Wang & Taitao Feng & Yifei Xin, 2021. "A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps," Mathematics, MDPI, vol. 9(3), pages 1-14, January.
    3. Bladt, Mogens & Ivanovs, Jevgenijs, 2021. "Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 105-123.
    4. Anna Castañer & M.Mercè Claramunt & Maite Mármol, 2014. "Some optimization and decision problems in proportional reinsurance," UB School of Economics Working Papers 2014/310, University of Barcelona School of Economics.
    5. Noh, Jungsik & Lee, Seung Y. & Lee, Sangyeol, 2012. "Quantile regression estimation for discretely observed SDE models with compound Poisson jumps," Economics Letters, Elsevier, vol. 117(3), pages 734-738.
    6. Lee, Wing Yan & Willmot, Gordon E., 2014. "On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 1-10.
    7. Vaios Dermitzakis & Konstadinos Politis, 2011. "Asymptotics for the Moments of the Time to Ruin for the Compound Poisson Model Perturbed by Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 749-761, December.
    8. Landriault, David & Shi, Tianxiang, 2015. "Occupation times in the MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 75-82.
    9. Cheung, Eric C.K. & Landriault, David, 2010. "A generalized penalty function with the maximum surplus prior to ruin in a MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 127-134, February.
    10. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    11. Jang Jiwook, 2009. "The Cost of Delay in a Mortgage/Credit Loan Portfolio," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(1), pages 1-14, November.
    12. A. S. Dibu & M. J. Jacob & Apostolos D. Papaioannou & Lewis Ramsden, 2021. "Delayed Capital Injections for a Risk Process with Markovian Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1057-1076, September.
    13. Lesław Gajek & Marcin Rudź, 2018. "Risk-switching insolvency models," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 51, pages 129-146.
    14. Ya Fang Wang & José Garrido & Ghislain Léveillé, 2018. "The Distribution of Discounted Compound PH–Renewal Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 69-96, March.
    15. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2019. "A generalised CIR process with externally-exciting and self-exciting jumps and its applications in insurance and finance," LSE Research Online Documents on Economics 102043, London School of Economics and Political Science, LSE Library.
    16. Liu, Baoliang & Wen, Yanqing & Qiu, Qingan & Shi, Haiyan & Chen, Jianhui, 2022. "Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    17. Jang, Jiwook & Mohd Ramli, Siti Norafidah, 2015. "Jump diffusion transition intensities in life insurance and disability annuity," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 440-451.
    18. Cheung, Eric C.K. & Zhu, Wei, 2023. "Cumulative Parisian ruin in finite and infinite time horizons for a renewal risk process with exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 84-101.
    19. Hansjörg Albrecher & José Carlos Araujo-Acuna, 2022. "On The Randomized Schmitter Problem," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 515-535, June.
    20. Cheung, Eric C.K. & Feng, Runhuan, 2013. "A unified analysis of claim costs up to ruin in a Markovian arrival risk model," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 98-109.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:crj:dpaper:2_2014. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Margherita Gallo The email address of this maintainer does not seem to be valid anymore. Please ask Margherita Gallo to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/crnavit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.