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Nonparametric analysis of aggregate loss models

Author

Listed:
  • J. M. Vilar
  • R. Cao
  • M. C. Ausin
  • C. Gonzalez-Fragueiro

Abstract

This paper describes a nonparametric approach to make inferences for aggregate loss models in the insurance framework. We assume that an insurance company provides a historical sample of claims given by claim occurrence times and claim sizes. Furthermore, information may be incomplete as claims may be censored and/or truncated. In this context, the main goal of this work consists of fitting a probability model for the total amount that will be paid on all claims during a fixed future time period. In order to solve this prediction problem, we propose a new methodology based on nonparametric estimators for the density functions with censored and truncated data, the use of Monte Carlo simulation methods and bootstrap resampling. The developed methodology is useful to compare alternative pricing strategies in different insurance decision problems. The proposed procedure is illustrated with a real dataset provided by the insurance department of an international commercial company.

Suggested Citation

  • J. M. Vilar & R. Cao & M. C. Ausin & C. Gonzalez-Fragueiro, 2009. "Nonparametric analysis of aggregate loss models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 149-166.
    • Handle: RePEc:taf:japsta:v:36:y:2009:i:2:p:149-166
    DOI: 10.1080/02664760802443921
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    References listed on IDEAS

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    1. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0501, December.
    2. C. Sánchez-Sellero & W. González-Manteiga & R. Cao, 1999. "Bandwidth Selection in Density Estimation with Truncated and Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 51-70, March.
    3. Bolance, Catalina & Guillen, Montserrat & Nielsen, Jens Perch, 2003. "Kernel density estimation of actuarial loss functions," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 19-36, February.
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    6. Hossack,I. B. & Pollard,J. H. & Zehnwirth,B., 1999. "Introductory Statistics with Applications in General Insurance," Cambridge Books, Cambridge University Press, number 9780521652346, November.
    7. Hossack,I. B. & Pollard,J. H. & Zehnwirth,B., 1999. "Introductory Statistics with Applications in General Insurance," Cambridge Books, Cambridge University Press, number 9780521655347, November.
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    9. Bolancé, Catalina & Guillén, Montserrat & Nielsen, Jens Perch, 2008. "Inverse beta transformation in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1757-1764, September.
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    Cited by:

    1. Jackson P. Lautier & Vladimir Pozdnyakov & Jun Yan, 2022. "Pricing Time-to-Event Contingent Cash Flows: A Discrete-Time Survival Analysis Approach," Papers 2201.04981, arXiv.org, revised Jan 2023.
    2. Baumgartner, Carolin & Gruber, Lutz F. & Czado, Claudia, 2015. "Bayesian total loss estimation using shared random effects," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 194-201.

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