4. Collective model

Given a portfolio of risks, the insurer seeks to evaluate and forecast the cumulative amount of claims likely to be generated by this portfolio over a future period, generally the following year. This assessment is based on a model representing this amount, which may be individual or collective. In the individual model, we consider a group of k risks and note X _i the amount of claims for risk i (i = 1, ..., k). The total amount of claims for this group is $X=X_1+\cdots +X_k$ , from which we deduce the pure premium $$