We are Living on the Edge: Managing Extreme‑Severity Claims Using Extreme Value Theory

Claims with high severity and low probability constitute a high risk for the insurance market. One tool to deal with this kind of event is the Extreme Value Theory (EVT). The main goal of this article is to apply the EVT to Actuarial Science using a different estimator for parameters, allowing the c...

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Bibliographic Details
Published inBrazilian business review Vol. 21; no. 3; pp. 1 - 22
Main Authors Carvalho, João Vinícius França, Oliveira, Luiz Henrique Alves
Format Journal Article
LanguageEnglish
Published Vitória FUCAPE Business School 17.05.2024
Fucape Business School
EditionEnglish ed.
Subjects
Actuarial science
Insurance companies
Insurance premiums
MANAGEMENT
Random variables
Reinsurance
Solvency
Statistics
Stochastic models
Insurance
Seguros
Expected shortfall
Valores extremos
High quantiles estimation
Estimação em altos quantis
Extreme values
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Summary:Claims with high severity and low probability constitute a high risk for the insurance market. One tool to deal with this kind of event is the Extreme Value Theory (EVT). The main goal of this article is to apply the EVT to Actuarial Science using a different estimator for parameters, allowing the calculation of pure reinsurance premiums and the choice for the retention limit for insurance companies. The execution was split into two parts: (i) comparing the estimators through simulations, and; (ii) using data from 5 SUSEP lines of business with different natures, intending to estimate some extreme value statistics. In simulation studies, the Pickands estimator was very promising, but the limited amount of data resulted in a great variance when applied to real cases. Lastly, we concluded that the EVT is a powerful tool for insurance, capturing the behavior of extreme clams amount better than traditional models
ISSN:1808-2386
1808-2386
DOI:10.15728/bbr.2022.1245.en