Frequency and Severity Modelling Using Multifractal Processes: An Application to Tornado Occurrence in the USA and CAT Bonds |
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Authors: | Donatien Hainaut Jean-Philippe Boucher |
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Institution: | 1. Rennes Business School-CREST, Rennes, France 2. Département de mathématiques, UQAM, Québec, Canada
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Abstract: | This paper proposes a statistical model for insurance claims arising from climatic events, such as tornadoes in the USA, that exhibit a large variability both in frequency and intensity. To represent this variability and seasonality, the claims process modelled by a Poisson process of intensity equal to the product of a periodic function, and a multifractal process is proposed. The size of claims is modelled in a similar way, with gamma random variables. This method is shown to enable simulation of the peak times of damage. A two-dimensional multifractal model is also investigated. The work concludes with an analysis of the impact of the model on the yield of weather bonds linked to damage caused by tornadoes. |
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