An Extension of Collective Risk Model for Stochastic Claim Reserving

The evaluation of outstanding claims uncertainty plays a fundamental role in managing insurance companies. This topic has gained an increasing interest over last years because of the development of a new capital requirement framework under the Solvency II project. In particular, as results of main Quantitative Impact Studies showed, reserve risk is an essential part of underwriting risks and it has a prominent weight on the capital requirement for non-life insurance companies. To this end, we provide here a stochastic methodology in order to evaluate the distribution of claims reserve and to quantify the capital requirement for reserve risk of a single line of business. This proposal extends some existing approaches (see [12], [13], [17] and [19]) and it could represent a viable alternative to well-known methodologies in literature. Finally, a detailed numerical analysis shows a comparison between the proposed methodology and the widely used bootstrapping based on Over-Dispersed Poisson model.