Abstract

Insurance is a risk transfer mechanism, which allows individuals and firms to reduce the uncertainty about their future cash flows. It provides financial compensation for the effects of misfortune through the establishment of a fund, into which all insured pay premiums and from which benefits are paid when insured events occur. These uncertainty is usually modeled through two distinct components the claim frequency and the claim severity, since in any given year, neither the number of claims nor their severity is known in advance. The usual stochastic insurance model is thus a random sum called the aggregate claims, where the random number of variables summed represents the claim frequency, while each variable summed represents the claims severities. Each play an important role in the model. Usually it is difficult to obtain the exact aggregate claims distribution, although it is important to researchers and practitioners in actuarial science. Several approximations have been suggested to this purpose. In particular, Chaubey et al. [3] proposed a new inverse gaussian-gamma mixture approximation. The main goal of this thesis is to study approximation methods to calculate stop-loss reinsurance premiums, including a proposal based on the inverse gaussian-gamma mixture approximation. Various graphical and numerical illustrations are given in support of our conclusions.