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Loss Distributions

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  • Burnecki, Krzysztof
  • Misiorek, Adam
  • Weron, Rafal

Abstract

This paper is intended as a guide to statistical inference for loss distributions. There are three basic approaches to deriving the loss distribution in an insurance risk model: empirical, analytical, and moment based. The empirical method is based on a sufficiently smooth and accurate estimate of the cumulative distribution function (cdf) and can be used only when large data sets are available. The analytical approach is probably the most often used in practice and certainly the most frequently adopted in the actuarial literature. It reduces to finding a suitable analytical expression which fits the observed data well and which is easy to handle. In some applications the exact shape of the loss distribution is not required. We may then use the moment based approach, which consists of estimating only the lowest characteristics (moments) of the distribution, like the mean and variance. Having a large collection of distributions to choose from, we need to narrow our selection to a single model and a unique parameter estimate. The type of the objective loss distribution can be easily selected by comparing the shapes of the empirical and theoretical mean excess functions. Goodness-of-fit can be verified by plotting the corresponding limited expected value functions. Finally, the hypothesis that the modeled random event is governed by a certain loss distribution can be statistically tested.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22163.

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Date of creation: 2010
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Handle: RePEc:pra:mprapa:22163

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Keywords: Loss distribution; Insurance risk model; Random variable generation; Goodness-of-fit testing; Mean excess function; Limited expected value function;

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References

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  1. Burnecki, Krzysztof & Weron, Rafal, 2010. "Simulation of Risk Processes," MPRA Paper 25444, University Library of Munich, Germany.
  2. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE) 2004,32, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  3. Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trück & Rafał Weron, 2006. "Modelling catastrophe claims with left-truncated severity distributions," Computational Statistics, Springer, Springer, vol. 21(3), pages 537-555, December.
  4. L'Ecuyer, Pierre, 2004. "Random number generation," Papers, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE) 2004,21, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  5. Krzysztof Burnecki & Rafal Weron, 2006. "Visualization tools for insurance risk processes," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/06/06, Hugo Steinhaus Center, Wroclaw University of Technology.
  6. Krzysztof Burnecki & Grzegorz Kukla & Rafal Weron, 2000. "Property insurance loss distributions," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/00/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  7. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
  8. Wolfgang Karl Härdle & Yuichi Mori & Jürgen Symanzik, 2012. "Computational Statistics (Journal)," SFB 649 Discussion Papers SFB649DP2012-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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Citations

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Cited by:
  1. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2012. "Skew mixture models for loss distributions: A Bayesian approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 617-623.
  2. Chernobai, Anna & Burnecki, Krzysztof & Rachev, Svetlozar & Trueck, Stefan & Weron, Rafal, 2005. "Modelling catastrophe claims with left-truncated severity distributions (extended version)," MPRA Paper 10423, University Library of Munich, Germany.
  3. Krzysztof Burnecki & Rafal Weron, 2006. "Visualization tools for insurance risk processes," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/06/06, Hugo Steinhaus Center, Wroclaw University of Technology.
  4. Weron, Rafał & Burnecki, Krzysztof, 2004. "Modeling the risk process in the XploRe computing environment," Papers, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE) 2004,08, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  5. Haerdle, Wolfgang & Cabrera, Brenda Lopez, 2007. "Calibrating CAT bonds for Mexican earthquakes," 101st Seminar, July 5-6, 2007, Berlin Germany, European Association of Agricultural Economists 9265, European Association of Agricultural Economists.
  6. Krzysztof Burnecki & Joanna Janczura & Rafal Weron, 2010. "Building Loss Models," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/10/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  7. Agnieszka Wylomanska, 2011. "Measures of dependence for Ornstein–Uhlenbeck processes with tempered stable distribution," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/11/04, Hugo Steinhaus Center, Wroclaw University of Technology.
  8. Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trück & Rafał Weron, 2006. "Modelling catastrophe claims with left-truncated severity distributions," Computational Statistics, Springer, Springer, vol. 21(3), pages 537-555, December.
  9. Sasa Zikovic, 2011. "Measuring risk of crude oil at extreme quantiles," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics, vol. 29(1), pages 9-31.

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