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March 2020 Regression for copula-linked compound distributions with applications in modeling aggregate insurance claims
Peng Shi, Zifeng Zhao
Ann. Appl. Stat. 14(1): 357-380 (March 2020). DOI: 10.1214/19-AOAS1299

Abstract

In actuarial research a task of particular interest and importance is to predict the loss cost for individual risks so that informative decisions are made in various insurance operations such as underwriting, ratemaking and capital management. The loss cost is typically viewed to follow a compound distribution where the summation of the severity variables is stopped by the frequency variable. A challenging issue in modeling such outcomes is to accommodate the potential dependence between the number of claims and the size of each individual claim. In this article we introduce a novel regression framework for compound distributions that uses a copula to accommodate the association between the frequency and the severity variables and, thus, allows for arbitrary dependence between the two components. We further show that the new model is very flexible and is easily modified to account for incomplete data due to censoring or truncation. The flexibility of the proposed model is illustrated using both simulated and real data sets. In the analysis of granular claims data from property insurance, we find substantive negative relationship between the number and the size of insurance claims. In addition, we demonstrate that ignoring the frequency-severity association could lead to biased decision-making in insurance operations.

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Peng Shi. Zifeng Zhao. "Regression for copula-linked compound distributions with applications in modeling aggregate insurance claims." Ann. Appl. Stat. 14 (1) 357 - 380, March 2020. https://doi.org/10.1214/19-AOAS1299

Information

Received: 1 August 2018; Revised: 1 August 2019; Published: March 2020
First available in Project Euclid: 16 April 2020

zbMATH: 07200175
MathSciNet: MR4085097
Digital Object Identifier: 10.1214/19-AOAS1299

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.14 • No. 1 • March 2020
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