IDEAS home Printed from https://ideas.repec.org/a/ijb/journl/v6y2007i3p225-236.html
   My bibliography  Save this article

A Markov Chain Monte Carlo Approach to Estimate the Risks of Extremely Large Insurance Claims

Author

Listed:
  • Wan-Kai Pang

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong)

  • Shui-Hung Hou

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong)

  • Marvin D. Troutt

    (Department of Management and Information Systems, Kent State University, U.S.A.)

  • Wing-Tong Yu

    (School of Accounting and Finance, The Hong Kong Polytechnic University, Hong Kong)

  • Ken W. K. Li

    (Department of Information and Communications Technology, The Hong Kong Institute of Vocational Education, Hong Kong)

Abstract

The Pareto distribution is a heavy-tailed distribution often used in actuarial models. It is important for modeling losses in insurance claims, especially when we used it to calculate the probability of an extreme event. Traditionally, maximum likelihood is used for parameter estimation, and we use the estimated parameters to calculate the tail probability Pr(X>c) where c is a large value. In this paper, we propose a Bayesian method to calculate the probability of this event. Markov Chain Monte Carlo techniques are employed to calculate the Pareto parameters.

Suggested Citation

  • Wan-Kai Pang & Shui-Hung Hou & Marvin D. Troutt & Wing-Tong Yu & Ken W. K. Li, 2007. "A Markov Chain Monte Carlo Approach to Estimate the Risks of Extremely Large Insurance Claims," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 6(3), pages 225-236, December.
    • Handle: RePEc:ijb:journl:v:6:y:2007:i:3:p:225-236
    as

    Download full text from publisher

    File URL: https://ijbe.fcu.edu.tw/assets/ijbe/past_issue/No.06-3/pdf/vol_6-3-4.pdf
    Download Restriction: no
    File URL: https://ijbe.fcu.edu.tw/assets/ijbe/past_issue/No.06-3/abstract/04.html
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Landsman, Zinoviy & Sherris, Michael, 2001. "Risk measures and insurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 103-115, August.
    2. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    3. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
    4. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    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. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    2. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
    3. López-Díaz, Miguel & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "On the Lp-metric between a probability distribution and its distortion," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 257-264.
    4. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
    5. Lin, Feng & Peng, Liang & Xie, Jiehua & Yang, Jingping, 2018. "Stochastic distortion and its transformed copula," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 148-166.
    6. Alexis Bienvenüe & Didier Rullière, 2012. "Iterative Adjustment of Survival Functions by Composed Probability Distortions," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(2), pages 156-179, September.
    7. Dilip B. Madan & Yazid M. Sharaiha, 2015. "Option overlay strategies," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1175-1190, July.
    8. John A. Major & Stephen J. Mildenhall, 2020. "Pricing and Capital Allocation for Multiline Insurance Firms With Finite Assets in an Imperfect Market," Papers 2008.12427, arXiv.org.
    9. Antonella Campana & Paola Ferretti, 2005. "Distortion Risk Measures and Discrete Risks," Game Theory and Information 0510013, University Library of Munich, Germany.
    10. Jones, Bruce L. & Puri, Madan L. & Zitikis, Ricardas, 2006. "Testing hypotheses about the equality of several risk measure values with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 253-270, April.
    11. Landsman, Zinoviy & Makov, Udi, 2012. "Translation-invariant and positive-homogeneous risk measures and optimal portfolio management in the presence of a riskless component," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 94-98.
    12. Antonella Campana & Paola Ferretti, 2008. "Bounds for Concave Distortion Risk Measures for Sums of Risks," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods in Insurance and Finance, pages 43-51, Springer.
    13. Xiaoqing Liang & Ruodu Wang & Virginia Young, 2021. "Optimal Insurance to Maximize RDEU Under a Distortion-Deviation Premium Principle," Papers 2107.02656, arXiv.org, revised Feb 2022.
    14. Hurlimann, Werner, 2001. "Distribution-free comparison of pricing principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 351-360, June.
    15. Li, Xiaohu & Lin, Jianhua, 2011. "Stochastic orders in time transformed exponential models with applications," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 47-52, July.
    16. Mierzejewski, Fernando, 2007. "The Short-Run Monetary Equilibrium with Liquidity Constraints," MPRA Paper 6526, University Library of Munich, Germany.
    17. Soren Bettels & Stefan Weber, 2024. "An Integrated Approach to Importance Sampling and Machine Learning for Efficient Monte Carlo Estimation of Distortion Risk Measures in Black Box Models," Papers 2408.02401, arXiv.org.
    18. Choo, Weihao & de Jong, Piet, 2009. "Loss reserving using loss aversion functions," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 271-277, October.
    19. Hernández Solís, Montserrat & Lozano Colomer, Cristina & Vilar Zanón, José Luis, 2013. "La prima de riesgo recargada en un seguro de rentas: tarificación mediante el uso de una medida de riesgo coherente || The Risk Recharged Premium for a Survival Life Insurance: Recharged Premium throu," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 15(1), pages 151-167, June.
    20. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, December.

    More about this item

    Keywords

    heavy-tail distributions; loss distribution model; Pareto probability distribution; Gibbs sampler;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:ijb:journl:v:6:y:2007:i:3:p:225-236. 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: Szu-Hsien Ho (email available below). General contact details of provider: https://edirc.repec.org/data/cbfcutw.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.