IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v9y2021i3p52-d515903.html
   My bibliography  Save this article

Quantifying the Role of Occurrence Losses in Catastrophe Excess of Loss Reinsurance Pricing

Author

Listed:
  • Shree Khare

    (Risk Management Solutions, The Minster Building, 21 Mincing Lane, London EC3R 7AG, UK
    These authors contributed equally to this work.)

  • Keven Roy

    (Hiscox, 1 Great St. Helen’s, London EC3A 6HX, UK
    These authors contributed equally to this work.)

Abstract

The aim of this paper is to merge order statistics with natural catastrophe reinsurance pricing to develop new theoretical and practical insights relevant to market practice and model development. We present a novel framework to quantify the role that occurrence losses (order statistics) play in pricing of catastrophe excess of loss (catXL) contracts. Our framework enables one to analytically quantify the contribution of a given occurrence loss to the mean and covariance structure, before and after the application of a catXL contract. We demonstrate the utility of our framework with an application to idealized catastrophe models for a multi-peril and a hurricane-only case. For the multi-peril case, we show precisely how contributions to so-called lower layers are dominated by high frequency perils, whereas higher layers are dominated by low-frequency high severity perils. Our framework enables market practitioners and model developers to assess and understand the impact of altered model assumptions on the role of occurrence losses in catXL pricing.

Suggested Citation

  • Shree Khare & Keven Roy, 2021. "Quantifying the Role of Occurrence Losses in Catastrophe Excess of Loss Reinsurance Pricing," Risks, MDPI, vol. 9(3), pages 1-40, March.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:3:p:52-:d:515903
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/9/3/52/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/9/3/52/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kenneth A. Froot, 1999. "The Financing of Catastrophe Risk," NBER Books, National Bureau of Economic Research, Inc, number froo99-1, May.
    2. Haroon M. Barakat & Mouhamed A. El-Shandidy, 2004. "Order statistics with random sample size," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 233-246.
    3. J. M. Buhrman, 1973. "On order statistics when the sample size has a binomial distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 27(3), pages 125-126, September.
    4. Shi, Peng & Feng, Xiaoping & Ivantsova, Anastasia, 2015. "Dependent frequency–severity modeling of insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 417-428.
    5. Hürlimann, Werner, 2005. "Excess of Loss Reinsurance with Reinstatements Revisited," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 211-238, May.
    6. P.C. Consul, 1984. "On The Distributions Of Order Statistics For A Random Sample Size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(4), pages 249-256, December.
    7. Mata, Ana J., 2000. "Pricing Excess of Loss Reinsurance with Reinstatements," ASTIN Bulletin, Cambridge University Press, vol. 30(2), pages 349-368, November.
    8. D. Gupta & R. C. Gupta, 1984. "On The Distribution Of Order Statistics For A Random Sample Size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(1), pages 13-19, March.
    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. Hilda Azkiyah Surya & Herlina Napitupulu & Sukono, 2023. "Double Risk Catastrophe Reinsurance Premium Based on Houses Damaged and Deaths," Mathematics, MDPI, vol. 11(4), pages 1-18, February.

    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. Paola Ferretti & Antonella Campana, 2011. "XL reinsurance with reinstatements and initial premium feasibility in exchangeability hypothesis," Working Papers 2011_14, Department of Economics, University of Venice "Ca' Foscari".
    2. Abdel-Aty Y. & Franz J. & Mahmoud M. A. W., 2003. "Bayesian Predictions for Exponentially Distributed Failure Times With One Change-Point," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 195-207, January.
    3. Vasileios M. Koutras & Markos V. Koutras, 2020. "Exact Distribution of Random Order Statistics and Applications in Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1539-1558, December.
    4. J. David Cummins & Michael Suher & George Zanjani, 1975. "Federal Financial Exposure to Natural Catastrophe Risk," NBER Chapters, in: Measuring and Managing Federal Financial Risk, pages 61-92, National Bureau of Economic Research, Inc.
    5. J. David Cummins & Christopher M. Lewis, 2002. "Catastrophic Events, Parameter Uncertainty and the Breakdown of Implicit Long-term Contracting in the Insurance Market: The Case of Terrorism Insurance," Center for Financial Institutions Working Papers 02-40, Wharton School Center for Financial Institutions, University of Pennsylvania.
    6. Zeinhum F. Jaheen, 2001. "Bayesian prediction for the Burr model with outliers and Random sample size," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 217-230.
    7. Steven Shavell, 2014. "A General Rationale for a Governmental Role in the Relief of Large Risks," NBER Working Papers 20192, National Bureau of Economic Research, Inc.
    8. Castañer, A. & Claramunt, M.M. & Lefèvre, C., 2013. "Survival probabilities in bivariate risk models, with application to reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 632-642.
    9. Ramon Alemany & Catalina Bolancé & Roberto Rodrigo & Raluca Vernic, 2020. "Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence—An Application to Model Claim Frequency and Optimal Transformed Average Severity," Mathematics, MDPI, vol. 9(1), pages 1-18, December.
    10. K. Goda & H. P. Hong, 2008. "Implied Preference for Seismic Design Level and Earthquake Insurance," Risk Analysis, John Wiley & Sons, vol. 28(2), pages 523-537, April.
    11. Brown, Jeffrey R. & Cummins, J. David & Lewis, Christopher M. & Wei, Ran, 2004. "An empirical analysis of the economic impact of federal terrorism reinsurance," Journal of Monetary Economics, Elsevier, vol. 51(5), pages 861-898, July.
    12. Al-Mutairi, D.K. & Ghitany, M.E. & Gupta, Ramesh C., 2011. "Estimation of reliability in a series system with random sample size," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 964-972, February.
    13. Froot, Kenneth A., 2001. "The market for catastrophe risk: a clinical examination," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 529-571, May.
    14. Markus K. Brunnermeier & Stefan Nagel & Lasse H. Pedersen, 2009. "Carry Trades and Currency Crashes," NBER Chapters, in: NBER Macroeconomics Annual 2008, Volume 23, pages 313-347, National Bureau of Economic Research, Inc.
    15. Zhiguo He & Arvind Krishnamurthy, 2013. "Intermediary Asset Pricing," American Economic Review, American Economic Association, vol. 103(2), pages 732-770, April.
    16. Torben Andersen, 2001. "Managing Economic Exposures of Natural Disasters: Exploring Alternative Financial Risk Management Opportunities and Instruments," IDB Publications (Working Papers) 8934, Inter-American Development Bank.
    17. Nabil Kazi-Tani, 2020. "Indifference Pricing of Reinsurance with Reinstatements Using Coherent Monetary Criteria," Working Papers hal-01742638, HAL.
    18. El-Adll, Magdy E., 2011. "Predicting future lifetime based on random number of three parameters Weibull distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1842-1854.
    19. M. Boyer & Charles Nyce, 2013. "An Industrial Organization Theory of Risk Sharing," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(4), pages 283-296.
    20. Ignacio Moreno & Purificación Parrado‐Martínez & Antonio Trujillo‐Ponce, 2020. "Economic crisis and determinants of solvency in the insurance sector: new evidence from Spain," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 60(3), pages 2965-2994, September.

    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:gam:jrisks:v:9:y:2021:i:3:p:52-:d:515903. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.