Handling the Dependence of Claim Severities with Copula Models

Problem statement: Several studies have been carried out on the modeling of claim severity data in actuarial literature as well as in insurance practice. Since it is well established that the claim cost distributions generally have positive support and are positively skewed, the regression models of Gamma and Lognormal have been used by practitioners for modeling claim severities. However, the fitting of claim severities via regression models assumes that the claim types are independent. Approach: In this study, independent assumption between claim types will be investigated as we will consider three types of Malaysian motor insurance claims namely Third Party Body Injury (TPBI), Third Party Property Damage (TPPD) and Own Damage (OD) and applied the normal, t, Frank and Clayton copulas for modeling dependence structures between these claim types. Results: The AIC and BIC indicated that the Clayton is the best copula for modeling dependence between TPBI and OD claims and between TPPD and OD claims, whereas the t-copula is the best copula for modeling dependence between TPBI and TPPD claims. Conclusion: This study modeled the dependence between insurance claim types using copulas on the Malaysian motor insurance claim severity data. The main advantage of using copula is that each marginal distribution can be specified independently based on the distribution of individual variable and then joined by the copula which takes into account the dependence between these variables. Based on the results, the estimated of copula parameter for claim severities indicate that the dependence between claim types is significant.