IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v51y2012i1p43-52.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668712000182
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2012.02.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Abstract: Capital Market Equilibrium in a Mean-Lower Partial Moment Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 635-635, November.
    2. Harlow, W. V. & Rao, Ramesh K. S., 1989. "Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 285-311, September.
    3. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
    4. Grootveld, Henk & Hallerbach, Winfried, 1999. "Variance vs downside risk: Is there really that much difference?," European Journal of Operational Research, Elsevier, vol. 114(2), pages 304-319, April.
    5. Simon Lee & X. Lin, 2010. "Modeling and Evaluating Insurance Losses Via Mixtures of Erlang Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(1), pages 107-130.
    6. Bladt, Mogens, 2005. "A Review on Phase-type Distributions and their Use in Risk Theory," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 145-161, May.
    7. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2025. "Hidden semi-Markov models for rainfall-related insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 91-106.
    6. 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.
    7. 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.
    8. 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.
    9. Tzougas, George & Jeong, Himchan, 2021. "An expectation-maximization algorithm for the exponential-generalized inverse Gaussian regression model with varying dispersion and shape for modelling the aggregate claim amount," LSE Research Online Documents on Economics 108210, London School of Economics and Political Science, LSE Library.
    10. Punzo, Antonio & Bagnato, Luca & Maruotti, Antonello, 2018. "Compound unimodal distributions for insurance losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 95-107.
    11. 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.
    12. Kartik Sethi & Siddhartha P. Chakrabarty, 2021. "Modeling premiums of non-life insurance companies in India," Papers 2106.02446, arXiv.org.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Fung, Tsz Chai & Badescu, Andrei L. & Lin, X. Sheldon, 2019. "A class of mixture of experts models for general insurance: Theoretical developments," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 111-127.

    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. Fulga, Cristinca, 2016. "Portfolio optimization under loss aversion," European Journal of Operational Research, Elsevier, vol. 251(1), pages 310-322.
    2. Ayub, Usman & Shah, Syed Zulfiqar Ali & Abbas, Qaisar, 2015. "Robust analysis for downside risk in portfolio management for a volatile stock market," Economic Modelling, Elsevier, vol. 44(C), pages 86-96.
    3. Wong, Man Hong, 2013. "Investment models based on clustered scenario trees," European Journal of Operational Research, Elsevier, vol. 227(2), pages 314-324.
    4. Ángel León & Manuel Moreno, 2015. "Lower Partial Moments under Gram Charlier Distribution: Performance Measures and Efficient Frontiers," QM&ET Working Papers 15-3, University of Alicante, D. Quantitative Methods and Economic Theory.
    5. Anthonisz, Sean A., 2012. "Asset pricing with partial-moments," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2122-2135.
    6. Cumova, Denisa & Nawrocki, David, 2011. "A symmetric LPM model for heuristic mean-semivariance analysis," Journal of Economics and Business, Elsevier, vol. 63(3), pages 217-236, May.
    7. Robert Jarrow & Feng Zhao, 2006. "Downside Loss Aversion and Portfolio Management," Management Science, INFORMS, vol. 52(4), pages 558-566, April.
    8. Dipankar Mondal & N. Selvaraju, 2022. "Convexity, two-fund separation and asset ranking in a mean-LPM portfolio selection framework," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 225-248, March.
    9. Elie Matta & Jean McGuire, 2008. "Too Risky to Hold? The Effect of Downside Risk, Accumulated Equity Wealth, and Firm Performance on CEO Equity Reduction," Organization Science, INFORMS, vol. 19(4), pages 567-580, August.
    10. Yuanyao Ding & Bo Zhang, 2009. "Risky asset pricing based on safety first fund management," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 353-361.
    11. Brogan, Anita J. & Stidham Jr., Shaler, 2008. "Non-separation in the mean-lower-partial-moment portfolio optimization problem," European Journal of Operational Research, Elsevier, vol. 184(2), pages 701-710, January.
    12. Zhangxin (Frank) Liu & Michael J. O'Neill, 2018. "Partial moment volatility indices," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 58(1), pages 195-215, March.
    13. Toker Doganoglu & Christoph Hartz & Stefan Mittnik, 2007. "Portfolio optimization when risk factors are conditionally varying and heavy tailed," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 333-354, May.
    14. Atilgan, Yigit & Bali, Turan G. & Demirtas, K. Ozgur & Gunaydin, A. Doruk, 2019. "Global downside risk and equity returns," Journal of International Money and Finance, Elsevier, vol. 98(C), pages 1-1.
    15. Botshekan, Mahmoud & Kraeussl, Roman & Lucas, Andre, 2012. "Cash Flow and Discount Rate Risk in Up and Down Markets: What Is Actually Priced?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(6), pages 1279-1301, December.
    16. Babak Eftekhari, 1998. "Lower partial moment hedge ratios," Applied Financial Economics, Taylor & Francis Journals, vol. 8(6), pages 645-652.
    17. Jose Fernandes & Augusto Hasman & Juan Ignacio Pena, 2007. "Risk premium: insights over the threshold," Applied Financial Economics, Taylor & Francis Journals, vol. 18(1), pages 41-59.
    18. López-Espinosa, Germán & Moreno, Antonio & Rubia, Antonio & Valderrama, Laura, 2015. "Systemic risk and asymmetric responses in the financial industry," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 471-485.
    19. Tamara Teplova & Evgeniya Shutova, 2011. "A Higher Moment Downside Framework for Conditional and Unconditional Capm in the Russian Stock Market," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 1(2), pages 157-178, December.
    20. Brychykova, A., 2019. "Capital Asset Pricing Model Using Fuzzy Data and Application for the Russian Stock Market," Journal of the New Economic Association, New Economic Association, vol. 43(3), pages 58-77.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:insuma:v:51:y:2012:i:1:p:43-52. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.