IDEAS home Printed from https://ideas.repec.org/p/icr/wpmath/19-2007.html
   My bibliography  Save this paper

Exchangeable Claims Sizes in a Compound Poisson Type Proces

Author

Listed:
  • Ramsés H. Mena
  • Luis E. Nieto-Barajas

Abstract

When dealing with risk models the typical assumption of independence among claim size distributions is not always satisfied. Here we consider the case when the claim sizes are exchangeable and study the implications when constructing aggregated claims through compound Poisson type processes. In par- ticular, exchangeability is achieved through conditional independence and using parametric and nonparametric measures for the conditioning distribution. A full Bayesian analysis of the proposed model is carried out to illustrate.

Suggested Citation

  • Ramsés H. Mena & Luis E. Nieto-Barajas, 2007. "Exchangeable Claims Sizes in a Compound Poisson Type Proces," ICER Working Papers - Applied Mathematics Series 19-2007, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:19-2007
    as

    Download full text from publisher

    File URL: http://www.bemservizi.unito.it/repec/icr/wp2007/ICERwp19-07.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Thomas Kaiser & Vytaras Brazauskas, 2006. "Interval Estimation of Actuarial Risk Measures," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 249-268.
    2. Ramsés H. Mena & Stephen G. Walker, 2005. "Stationary Autoregressive Models via a Bayesian Nonparametric Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 789-805, November.
    3. Gerber, Hans U., 1982. "Ruin theory in the linear model," Insurance: Mathematics and Economics, Elsevier, vol. 1(3), pages 213-217, July.
    4. Daboni, Luciano, 1974. "Some Models of Inference in the Risk Theory from a Bayesian Viewpoint," ASTIN Bulletin, Cambridge University Press, vol. 8(1), pages 38-56, September.
    5. Cossette, Helene & Marceau, Etienne, 2000. "The discrete-time risk model with correlated classes of business," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 133-149, 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. Zhang, Zhiqiang & Yuen, Kam C. & Li, Wai Keung, 2007. "A time-series risk model with constant interest for dependent classes of business," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 32-40, July.
    2. Albrecher Hansjörg & Kantor Josef, 2002. "Simulation of ruin probabilities for risk processes of Markovian type," Monte Carlo Methods and Applications, De Gruyter, vol. 8(2), pages 111-128, December.
    3. Yuen, Kam C. & Guo, Junyi & Wu, Xueyuan, 2006. "On the first time of ruin in the bivariate compound Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 298-308, April.
    4. Wang, Guojing & Yuen, Kam C., 2005. "On a correlated aggregate claims model with thinning-dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 456-468, June.
    5. He Liu & Zhenhua Bao, 2015. "On a Discrete Interaction Risk Model with Delayed Claims," JRFM, MDPI, vol. 8(4), pages 1-14, September.
    6. Yuen, Kam C. & Guo, Junyi & Wu, Xueyuan, 2002. "On a correlated aggregate claims model with Poisson and Erlang risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 205-214, October.
    7. Bai, Lihua & Cai, Jun & Zhou, Ming, 2013. "Optimal reinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 664-670.
    8. Yingxu Tian & Zhongyang Sun, 2018. "Mean-Variance Portfolio Selection in a Jump-Diffusion Financial Market with Common Shock Dependence," JRFM, MDPI, vol. 11(2), pages 1-12, May.
    9. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    10. Araichi, Sawssen & Peretti, Christian de & Belkacem, Lotfi, 2016. "Solvency capital requirement for a temporal dependent losses in insurance," Economic Modelling, Elsevier, vol. 58(C), pages 588-598.
    11. Martínez-Ovando Juan Carlos & Walker Stephen G., 2011. "Time-series Modelling, Stationarity and Bayesian Nonparametric Methods," Working Papers 2011-08, Banco de México.
    12. Yinghui Dong & Kam C. Yuen & Guojing Wang & Chongfeng Wu, 2016. "A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 459-486, June.
    13. Zhengyan Lin & Xinmei Shen, 2013. "Approximation of the Tail Probability of Dependent Random Sums Under Consistent Variation and Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 165-186, March.
    14. Romain Biard & Claude Lefèvre & Stéphane Loisel, 2008. "Impact of correlation crises in risk theory," Post-Print hal-00308782, HAL.
    15. Isadora Antoniano-Villalobos & Stephen G. Walker, 2016. "A Nonparametric Model for Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 126-142, January.
    16. Biard, Romain & Lefèvre, Claude & Loisel, Stéphane, 2008. "Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 412-421, December.
    17. Hélène Cossette & Etienne Marceau & Véronique Maume-Deschamps, 2011. "Adjustment Coefficient for Risk Processes in Some Dependent Contexts," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 695-721, December.
    18. Cossette, Hélène & Marceau, Étienne & Toureille, Florent, 2011. "Risk models based on time series for count random variables," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 19-28, January.
    19. Xiang Hu & Lianzeng Zhang, 2016. "Ruin Probability in a Correlated Aggregate Claims Model with Common Poisson Shocks: Application to Reinsurance," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 675-689, September.
    20. Dang, Lanfen & Zhu, Ning & Zhang, Haiming, 2009. "Survival probability for a two-dimensional risk model," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 491-496, June.

    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:icr:wpmath:19-2007. 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: Daniele Pennesi (email available below). General contact details of provider: https://edirc.repec.org/data/icerrit.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.