Large Deviation Bounds of the Aggregate Claims Under Varying Tail Distributions

The study of tail behaviour of insurance claims is very essential to the work of actuaries, as it helps in proper reserving and timely claim payout when it becomes necessary. It is therefore important to understand the tail behaviour of insurance claims in order not to underestimate associated risks, which can lead to ruin or bankruptcy of an insurance company. This work uses large deviations to examine the tail behaviour of insurance claims submitted by policy holders to an insurance company under varying tail distributions. We estimated explicit large deviation bounds under different assumptions of the tail distribution of claim amount with the assumption that the number of claims arriving at any given time follows a Poisson distribution at some given rate parameter. Both light and heavy tail distributions are considered for the claim distributions. The result shows different large deviation rate functions with varying speeds under the varying tail distributions.