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Tail index partition-based rules extraction with application to tornado damage insurance

Published online by Cambridge University Press:  22 February 2023

Arthur Maillart  and
Christian Y. Robert Open the ORCID record for Christian Y. Robert [Opens in a new window]
Arthur Maillart
Affiliation:
Detralytics, Paris, France Institut de Science Financière et d’Assurances, Université de Lyon, Université Lyon 1, 50 Avenue Tony Garnier, F-69007 Lyon, France
Christian Y. Robert*
Affiliation:
Laboratory in Finance and Insurance – LFA, CREST – Center for Research in Economics and Statistics, ENSAE Paris, France, Institut de Science Financière et d’Assurances, Université de Lyon, Université Lyon 1, 50 Avenue Tony Garnier, F-69007 Lyon, France
*
*Corresponding author. E-mail: christian.robert@univ-lyon1.fr
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Abstract

The tail index is an important parameter that measures how extreme events occur. In many practical cases, this tail index depends on covariates. In this paper,we assume that it takes a finite number of values over a partition of the covariate space. This article proposes a tail index partition-based rules extraction method that is able to construct estimates of the partition subsets and estimates of the tail index values. The method combines two steps: first an additive tree ensemble based on the Gamma deviance is fitted, and second a hierarchical clustering with spatial constraints is used to estimate the subsets of the partition. We also propose a global tree surrogate model to approximate the partition-based rules while providing an explainable model from the initial covariates. Our procedure is illustrated on simulated data. A real case study on wind property damages caused by tornadoes is finally presented.

Keywords

Tail indexadditive tree ensemblespartitioning methodsXAI
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 53 , Issue 2 , May 2023 , pp. 258 - 284
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The International Actuarial Association

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