R Programming for Actuarial Science

14 Copulas – A Modelling Exercise

Peter McQuire

library(MASS)
library(copula)
library(stats)

14.1 Introduction

In the previous chapter we looked at a number of fundamental concepts underlying copulas, together with various functions available in R which allow us to model multivariate data using copulas. In this chapter we develop those ideas to analyse a set of insurance claims data. The objective is to develop an appropriate copula model in respect of this data, estimate the level of future claims, and hence determine an appropriate amount of risk capital which the insurer should hold.

14.2 Modelling Future Claims

14.2.1 Data

The data we will use consists of total monthly claim amounts from the UK and US departments of an insurance company, spanning 200 months. We will use copulas to analyse any dependency pattern which may exist between UK and US claims. The process is similar to that set out in the previous chapter on copulas.

It is important not to lose sight of the company’s key objective in this example – to analyse the total, combined claim amounts from the UK and US departments which may be incurred next month or year. This in turn helps us to determine, amongst other things, the likely distribution of the company profits and the likelihood of company insolvency. The central idea here is that the pattern of the dependency between UK and US claims will affect the total monthly claims distribution.

Let’s download and plot the data (Figure 14.1):

Figure 14.1 UK and ...