Dependence modeling of frequency-severity of insurance claims using waiting time

Mixed copula approach has been used to jointly model discrete variable of claim counts and continuous variable of claim amounts. We propose to use a copula to link two continuous variables of the waiting time for the second claim and the average claim size. The frequency-severity dependence can be derived using the relationship between the waiting time and the counts of a Poisson process. Assuming a Gaussian copula and a log-normal distributed average claim size, we can investigate the effect of claim counts on the conditional claim severity analytically, which would be difficult in the mixed copula approach. We propose a Monte Carlo algorithm to simulate from the predictive distribution of the aggregated claims amount. In an empirical example, we illustrate the proposed method and compare with other competing methods. It shows that our proposed method provides quite competitive results.