EXCESS-LOSS FUNCTION IN DETERMINING REINSURANCE PREMIUM - (NIM : 20814022), AMELIA
One way for an insurance company to protect itself against the risk of large claims is to reinsure itself. An excess-of-loss reinsurance scheme is a reinsurance agreement with a reinsurance company (reinsurer) in which the reinsurer will pay the excess of the loss above a retention amount. In an excess-of-loss reinsurance, a reinsurer will manage the losses in layers. The layering system is established when a reinsurer or several reinsurance companies are willing to manage the excess of loss in diﬀerent layers. Consequently, a reinsurer (or reinsurers) needs to be able to determine the proper reinsurance premiums in order to set up enough technical reserves. Mathematically, the premium is determined using ground-up loss data. However, most of the time, a reinsurer is only able to obtained a payment-per-loss data. Halliwell (2012) introduced the excess-loss function which is powerful in determining the reinsurance premiums for each layer of losses. In this Thesis, the reinsurance premium is determined based on the expected value principle and the standard deviation principle which make use of the value of the excess-loss function, under the assumptions that the loss data follows a mixed exponential distribution or a lognormal distribution. Under the mixed exponential distribution assumption, the value of the excess-loss function is determined analytically and through simulation; where as under the lognormal distribution, it is determined only through simulation. It is found that under both distribution assumptions, the reinsurance premium obtained using the expected value principle is lesser than that obtained using the standard deviation principle for corresponding loading factors. In addition, the covariance and the correlation between layers indicate that there is a linear relationship or similar direction of correlation between layers; however, the correlation decreases as the layers are further apart.