Total loss estimation using copula-based regression models

By Nicole Kraemer, Eike C. Brechmann, D. Silvestrini, Claudia Czado. 2012

84 citations recorded by the source corpus.

We present a joint copula-based model for insurance claims and sizes. It uses bivariate copulae to accommodate for the dependence between these quantities. We derive the general distribution of the policy loss without the restrictive assumption of independence. We illustrate that this distribution tends to be skewed and multi-modal, and that an independence assumption can lead to substantial bias in the estimation of the policy loss. Further, we extend our framework to regression models by combining marginal generalized linear models with a copula. We show that this approach leads to a flexible class of models, and that the parameters can be estimated efficiently using maximum-likelihood. We propose a test procedure for the selection of the optimal copula family. The usefulness of our approach is illustrated in a simulation study and in an analysis of car insurance policies.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/03318172ee3a278e04e7d9df2e115a7fe4b6a6d8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

1. Lu Yang
2. Gee Y. Lee
3. Edward W. Frees
4. Jun Yan
5. Lluís Bermúdez
6. Dimitris Karlis

In Statistics and Probability

1. Lu Yang
2. Gee Y. Lee
3. Edward W. Frees
4. Jun Yan
5. Emiliano A. Valdez
6. Lluís Bermúdez
7. Dimitris Karlis

Citations in the corpus

• Multivariate Frequency-Severity Regression Models in Insurance (2016, background): “In [54], the distribution of policy loss is derived without the independence assumption between frequency and severity.”