Extreme value estimation of the conditional risk premium in reinsurance

Abstract In the paper we study the estimation of reinsurance premiums when the claim size is observed together with additional information in the form of random covariates. Using extreme value arguments, we propose an estimator for the risk premium conditional on a value for the covariate, and derive its asymptotic properties, after suitable normalization. The finite sample behavior is evaluated with a simulation experiment, and we apply the methodology to a dataset of automobile insurance claims from Australia.

[1]  A. Guillou,et al.  Local robust estimation of the Pickands dependence function , 2018, The Annals of Statistics.

[2]  J. Beirlant,et al.  On univariate extreme value statistics and the estimation of reinsurance premiums , 2006 .

[3]  Stéphane Girard,et al.  On the estimation of the functional Weibull tail-coefficient , 2016, J. Multivar. Anal..

[4]  J. Teugels,et al.  Statistics of Extremes , 2004 .

[5]  S. Girard,et al.  Functional kernel estimators of large conditional quantiles , 2011, 1107.2261.

[6]  Johan Segers,et al.  Second-order refined peaks-over-threshold modelling for heavy-tailed distributions , 2009, 0901.1518.

[7]  Jonathan El Methni,et al.  Kernel estimation of extreme regression risk measures , 2018 .

[8]  S. Girard,et al.  Kernel estimators of extreme level curves , 2011 .

[9]  Shaun S. Wang.  Premium Calculation by Transforming the Layer Premium Density , 1996, ASTIN Bulletin.

[10]  S. Girard,et al.  On kernel smoothing for extremal quantile regression , 2012, 1312.5123.

[11]  B. M. Hill,et al.  A Simple General Approach to Inference About the Tail of a Distribution , 1975 .

[12]  Armelle Guillou,et al.  Conditional marginal expected shortfall , 2021, Extremes.

[13]  J. Beirlant,et al.  HEAVY-TAILED DISTRIBUTIONS AND RATING , 2001 .

[14]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[15]  Armelle Guillou,et al.  A Weissman-type estimator of the conditional marginal expected shortfall , 2020, Econometrics and Statistics.

[16]  J. Teugels,et al.  Reinsurance: Actuarial and Statistical Aspects , 2017 .

[17]  A. Guillou,et al.  Bias-corrected estimation for conditional Pareto-type distributions with random right censoring , 2019, Extremes.

[18]  Jonathan El Methni,et al.  Non‐parametric Estimation of Extreme Risk Measures from Conditional Heavy‐tailed Distributions , 2014 .

[19]  A. Guillou,et al.  Local Estimation of the Conditional Stable Tail Dependence Function , 2018 .