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Modelling losses and locating the tail with the Pareto Positive Stable distribution

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  • Guillen, Montserrat
  • Prieto, Faustino
  • Sarabia, José María

Abstract

This paper focuses on modelling the severity distribution. We directly model the small, moderate and large losses with the Pareto Positive Stable (PPS) distribution and thus it is not necessary to fix a threshold for the tail behaviour. Estimation with the method of moments is straightforward. Properties, graphical tests and expressions for value-at risk and tail value-at-risk are presented. Furthermore, we show that the PPS distribution can be used to construct a statistical test for the Pareto distribution and to determine the threshold for the Pareto shape if required. An application to loss data is presented. We conclude that the PPS distribution can perform better than commonly used distributions when modelling a single loss distribution for moderate and large losses. This approach avoids the pitfalls of cut-off selection and it is very simple to implement for quantitative risk analysis.

Suggested Citation

  • Guillen, Montserrat & Prieto, Faustino & Sarabia, José María, 2011. "Modelling losses and locating the tail with the Pareto Positive Stable distribution," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 454-461.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:454-461
    DOI: 10.1016/j.insmatheco.2011.07.004
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    References listed on IDEAS

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    1. Cummins, J. David & Dionne, Georges & McDonald, James B. & Pritchett, B. Michael, 1990. "Applications of the GB2 family of distributions in modeling insurance loss processes," Insurance: Mathematics and Economics, Elsevier, vol. 9(4), pages 257-272, December.
    2. Bolance, Catalina & Guillen, Montserrat & Nielsen, Jens Perch, 2003. "Kernel density estimation of actuarial loss functions," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 19-36, February.
    3. Han, Zhongxian & Gau, Wu-Chyuan, 2008. "Estimation of loss reserves with lognormal development factors," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 389-395, February.
    4. Adelchi Azzalini, 2005. "The Skew-normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188.
    5. Frangos, Nikolaos & Karlis, Dimitris, 2004. "Modelling losses using an exponential-inverse Gaussian distribution," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 53-67, August.
    6. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.
    7. 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.
    8. H. Bauke, 2007. "Parameter estimation for power-law distributions by maximum likelihood methods," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(2), pages 167-173, July.
    9. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    10. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
    11. Bolance, Catalina & Guillen, Montserrat & Pelican, Elena & Vernic, Raluca, 2008. "Skewed bivariate models and nonparametric estimation for the CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 386-393, December.
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    Citations

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    Cited by:

    1. Sáez, Antonio José & Prieto, Faustino & Sarabia, José María, 2012. "A two-tail version of the PPS distribution with application to current account balance data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5160-5171.
    2. Urbina, Jilber & Guillén, Montserrat, 2013. "An application of capital allocation principles to operational risk," MPRA Paper 75726, University Library of Munich, Germany, revised Dec 2013.
    3. repec:hal:journl:hal-00880258 is not listed on IDEAS
    4. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 273-280.
    5. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2013. "“The use of flexible quantile-based measures in risk assessment”," IREA Working Papers 201323, University of Barcelona, Research Institute of Applied Economics, revised Dec 2013.
    6. Kratz , Marie, 2013. "There is a VaR Beyond Usual Approximations," ESSEC Working Papers WP1317, ESSEC Research Center, ESSEC Business School.
    7. Marie Kratz, 2013. "There is a VaR beyond usual approximations," Papers 1311.0270, arXiv.org.
    8. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 255-262.
    9. Belles-Sampera, Jaume & Guillen, Montserrat & Santolino, Miguel, 2016. "What attitudes to risk underlie distortion risk measure choices?," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 101-109.
    10. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers 2014-05, Universitat de Barcelona, UB Riskcenter.
    11. Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.
    12. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2015. "What attitudes to risk underlie distortion risk measure choices?," Working Papers 2015-05, Universitat de Barcelona, UB Riskcenter.
    13. Belles-Sampera, Jaume & Guillén, Montserrat & Santolino, Miguel, 2014. "GlueVaR risk measures in capital allocation applications," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 132-137.
    14. Lluís Bermúdez & Antoni Ferri & Montserrat Guillén, 2014. "On the use of risk measures in solvency capital estimation," International Journal of Business Continuity and Risk Management, Inderscience Enterprises Ltd, vol. 5(1), pages 4-13.
    15. Ramon ALEMANY & Catalina BOLANCÉ & Montserrat GUILLÉN & Alemar E. PADILLA-BARRETO, 2016. "Combining Parametric And Non-Parametric Methods To Compute Value-At-Risk," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(4), pages 61-74.
    16. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2013. "“Beyond Value-at-Risk: GlueVaR Distortion Risk Measures”," IREA Working Papers 201302, University of Barcelona, Research Institute of Applied Economics, revised Feb 2013.
    17. Marie Kratz, 2013. "There is a VaR Beyond Usual Approximations," Working Papers hal-00880258, HAL.

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