On the Moments of the Aggregate Discounted Claims with Dependence Between Inter-Arrival Times} \runtit{Moments of the aggregate discounted claims

F. Adekambi, F. Marri

2019, v.25, Issue 1, 149-169

ABSTRACT

In the classical collective insurance risk model, the independence among inter-arrival times
is one of the crucial assumptions. However, in reality, one could easily identify exceptions to this assumption. For instance, in car insurance, if there has been a long waiting time before a claim, the next inter-arrival time can also be long, either, because the policyholders are potentially good drivers; or 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 derive a recursive formula for the higher moments of the discounted aggregate renewal claims under these relaxed conditions.

Keywords: Archimedean copula; constant interest rate; discounted aggregate claims; joint moments; moment generating function; renewal process

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