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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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    Cited by:

    1. Jaume Belles‐Sampera & Montserrat Guillén & Miguel Santolino, 2014. "Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 121-134, January.
    2. repec:hal:journl:hal-00880258 is not listed on IDEAS
    3. Bolancé, Catalina & Bahraoui, Zuhair & Artís, Manuel, 2014. "Quantifying the risk using copulae with nonparametric marginals," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 46-56.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Kratz , Marie, 2013. "There is a VaR Beyond Usual Approximations," ESSEC Working Papers WP1317, ESSEC Research Center, ESSEC Business School.
    9. 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.
    10. Urbina, Jilber & Guillén, Montserrat, 2013. "An application of capital allocation principles to operational risk," Working Papers 2072/222201, Universitat Rovira i Virgili, Department of Economics.
    11. S. Chadjiconstantinidis & M. V. Koutras & F. S. Milienos, 2023. "The distribution of extended discrete random sums and its application to waiting time distributions," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.
    12. Marie Kratz, 2013. "There is a VaR beyond usual approximations," Papers 1311.0270, arXiv.org.
    13. 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.
    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. 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.
    16. 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.
    17. Faustino Prieto & José María Sarabia & Enrique Calderín-Ojeda, 2021. "The nonlinear distribution of employment across municipalities," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(2), pages 287-307, April.
    18. 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.
    19. 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.
    20. 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.
    21. Marie Kratz, 2013. "There is a VaR Beyond Usual Approximations," Working Papers hal-00880258, HAL.

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