Modelling Risk Dependencies in Insurance Using Survival Clayton Copula

Abstract

Our aim in this paper is to show the use of survival Clayton copula as a suitable tool for modelling risk dependencies in insurance. Apurpose-built simulation of an adequate upper tail dependence can be an important part of the aggregation of risks in an insurer’s internal models. The occurrence of extreme values of the aggregate random variable might have a very negative impact on the insurer when securing coverage of unexpected losses. The upper conditional quantile exceedance probability of the copula is a suitable indicator. In addition an analysis of its effect on the level of modelling of the risk scenario is available. This effect is measured using the Tail Value at Risk of the aggregate random variable. To simplify our description of the given principle for aggregating risks we will in this paper only consider the two-dimensional case. The programming language R was used to simulate the values of the joint distribution of the marginal random variables.

Keywords

• dependence modelling
• survival clayton copula
• conditional quantile exceedance probability
• joint distribution
• tail value at risk
• risk aggregation