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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. Kenneth A. Froot, 1999. "The Financing of Catastrophe Risk," NBER Books, National Bureau of Economic Research, Inc, number froo99-1, March.
    3. Mata, Ana J., 2000. "Pricing Excess of Loss Reinsurance with Reinstatements," ASTIN Bulletin, Cambridge University Press, vol. 30(2), pages 349-368, November.
    4. Hürlimann, Werner, 2005. "Excess of Loss Reinsurance with Reinstatements Revisited," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 211-238, May.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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    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.

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