Modeling Dependence Between Report Lag and Claim Amounts Using Copula Models

Abstract

Relationships between two or more variables are considered a phenomenon of interest in a world where modelling risk is becoming more and more popular. This is especially important for the insurance sector whose core business is protecting individuals from occurrences of risk. Some of the risks insurance companies face includes holding inefficient reserve amounts for claims policyholders take time to report. Having a variable that can explain the behavior of another can prove an important aid in understanding the variable of interest. In the case of insurance companies; establishing the relationship that claim amounts have to the time policyholders take to report the claim could help establish how much should be kept aside for claims not yet reported. This relationship is described as dependence between variables. The most common measure used to quantify dependence between variables is the Pearson’s correlation coefficient. This is a measure that requires the use of the covariance between the variables and their individual variances. However, the Pearson’s correlation coefficient is a measure that assumes linear dependence between variables. This limits the effectiveness of its use as a measure; since it cannot explain dependence in the case of a non-linear relationship. Furthermore the Pearson’s correlation coefficient is only a single figure and therefore limits the amount of information we can derive from it concerning the dependence between the variables. This leads us to the use of copulas as a measure of dependence between variables. Copulas; being distributions themselves; have the advantage of being able to portray more information concerning the dependence structures between the two variables. The following is a study that seeks to establish the relationship between claim amounts and the report delay period for claims in an insurance company using copulas