Trivariate Copula to Estimate Claim Costs: the Malaysian Motor Insurance Experience

Abstract

A road vehicle accident may produce three types of insurance claim namely third party bodily injury (TPBI), own damage (OD) and third party property damage (TPPD). If there is more than one claim type, the independent assumption between insurance claim types can lead to over- or underestimated claims. This study proposes the application of trivariate copula from Archimedean family, namely Clayton, Frank and Gumbel, with regression marginals, namely Gamma and inverse Gaussian, to model dependencies among claim types in the Malaysian motor insurance claim costs data. The results of AIC and BIC from independent models indicate that Gamma regression is better than inverse Gaussian regression for all claim types. The results of AIC, BIC, plot of empirical versus fitted copula and plot of intermediate variable distribution versus intermediate variable from dependent models imply that Frank copula is the best model for accommodating dependences among insurance claim types. The simulation results imply that independent models for both TPBI and TPPD claims produce larger number of risk classes with overestimated claims.