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A new class of models for heavy tailed distributions in finance and insurance risk

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  • Ahn, Soohan
  • Kim, Joseph H.T.
  • Ramaswami, Vaidyanathan

Abstract

Many insurance loss data are known to be heavy-tailed. In this article we study the class of Log phase-type (LogPH) distributions as a parametric alternative in fitting heavy tailed data. Transformed from the popular phase-type distribution class, the LogPH introduced by Ramaswami exhibits several advantages over other parametric alternatives. We analytically derive its tail related quantities including the conditional tail moments and the mean excess function, and also discuss its tail thickness in the context of extreme value theory. Because of its denseness proved herein, we argue that the LogPH can offer a rich class of heavy-tailed loss distributions without separate modeling for the tail side, which is the case for the generalized Pareto distribution (GPD). As a numerical example we use the well-known Danish fire data to calibrate the LogPH model and compare the result with that of the GPD. We also present fitting results for a set of insurance guarantee loss data.

Suggested Citation

  • Ahn, Soohan & Kim, Joseph H.T. & Ramaswami, Vaidyanathan, 2012. "A new class of models for heavy tailed distributions in finance and insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 43-52.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:43-52
    DOI: 10.1016/j.insmatheco.2012.02.002
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    2. Kartik Sethi & Siddhartha P. Chakrabarty, 2021. "Modeling premiums of non-life insurance companies in India," Papers 2106.02446, arXiv.org.
    3. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2023. "Hidden semi-Markov models for rainfall-related insurance claims," Discussion Papers 2023/17, Norwegian School of Economics, Department of Business and Management Science.
    4. Christian Biener & Martin Eling, 2013. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 16(2), pages 219-231, September.
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    6. Omer L. Gebizlioglu & Serap Yörübulut, 2016. "A Pseudo-Pareto Distribution and Concomitants of Its Order Statistics," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1043-1064, December.
    7. George Tzougas & Himchan Jeong, 2021. "An Expectation-Maximization Algorithm for the Exponential-Generalized Inverse Gaussian Regression Model with Varying Dispersion and Shape for Modelling the Aggregate Claim Amount," Risks, MDPI, vol. 9(1), pages 1-17, January.
    8. Hanieh Panahi, 2016. "Model Selection Test for the Heavy-Tailed Distributions under Censored Samples with Application in Financial Data," IJFS, MDPI, vol. 4(4), pages 1-14, December.
    9. Tzougas, George & Karlis, Dimitris, 2020. "An EM algorithm for fitting a new class of mixed exponential regression models with varying dispersion," LSE Research Online Documents on Economics 104027, London School of Economics and Political Science, LSE Library.
    10. Pavithra, Celeste R. & Deepak, T.G., 2022. "Parameter estimation and computation of the Fisher information matrix for functions of phase type random variables," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    11. 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.
    12. Antoine J.‐P. Tixier & Matthew R. Hallowell & Balaji Rajagopalan, 2017. "Construction Safety Risk Modeling and Simulation," Risk Analysis, John Wiley & Sons, vol. 37(10), pages 1917-1935, October.
    13. Kim, Joseph H.T. & Kim, Joocheol, 2015. "A parametric alternative to the Hill estimator for heavy-tailed distributions," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 60-71.
    14. Jeon, Yongho & Kim, Joseph H.T., 2013. "A gamma kernel density estimation for insurance loss data," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 569-579.
    15. Farias, Rafael B.A. & Montoril, Michel H. & Andrade, José A.A., 2016. "Bayesian inference for extreme quantiles of heavy tailed distributions," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 103-107.
    16. Park, Myung Hyun & Kim, Joseph H.T., 2016. "Estimating extreme tail risk measures with generalized Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 91-104.
    17. Vatamidou, E. & Adan, I.J.B.F. & Vlasiou, M. & Zwart, B., 2013. "Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 366-378.
    18. Punzo, Antonio & Bagnato, Luca & Maruotti, Antonello, 2018. "Compound unimodal distributions for insurance losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 95-107.
    19. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.

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