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Composite Lognormal–Pareto model with random threshold

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  • Mathieu Pigeon
  • Michel Denuit

Abstract

This paper further considers the composite Lognormal–Pareto model proposed by Cooray & Ananda (2005) and suitably modified by Scollnik (2007). This model is based on a Lognormal density up to an unknown threshold value and a Pareto density thereafter. Instead of using a single threshold value applying uniformly to the whole data set, the model proposed in the present paper allows for heterogeneity with respect to the threshold and let it vary among observations. Specifically, the threshold value for a particular observation is seen as the realization of a positive random variable and the mixed composite Lognormal–Pareto model is obtained by averaging over the population of interest. The performance of the composite Lognormal–Pareto model and of its mixed extension is compared using the well-known Danish fire losses data set.

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  • Mathieu Pigeon & Michel Denuit, 2011. "Composite Lognormal–Pareto model with random threshold," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2011(3), pages 177-192.
    • Handle: RePEc:taf:sactxx:v:2011:y:2011:i:3:p:177-192
    DOI: 10.1080/03461231003690754
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    Cited by:

    1. Sarra Ghaddab & Manel Kacem & Christian Peretti & Lotfi Belkacem, 2023. "Extreme severity modeling using a GLM-GPD combination: application to an excess of loss reinsurance treaty," Empirical Economics, Springer, vol. 65(3), pages 1105-1127, September.
    2. 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.
    3. Rocco Roberto Cerchiara & Francesco Acri, 2020. "Estimating the Volatility of Non-Life Premium Risk Under Solvency II: Discussion of Danish Fire Insurance Data," Risks, MDPI, vol. 8(3), pages 1-19, July.

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