Speaker(s): Franck Adekambi (University of Johannesbourg / CERAF)
In the classical collective insurance risk model, the independence among inter-claim times is one of the crucial assumptions. However, in reality, one could easily find violations of such assumption. For instance, in car insurance, if there has been a long waiting time before a claim, the next inter-arrival time can be long, as well, because the policyholders are potentially "good drivers"; or it could be the other way around, where some policyholders only start to use their cars a long time after purchasing them, then claims would suddenly arrive more frequently after a long silence. Hence, a shorter interval before the next claim can be expected. Therefore, a natural way to relax this assumption is to introduce a dependence structure in-between inter-arrival times, and that is the main purpose of this paper.