Impact of dependence among multiple claims in a single loss

In the collective risk model, the aggregate claim amount for the portfolio is denoted by S = X 1 + X 2 + … + X N where X i , i ≥ 1 , is the amount of loss resulting from the i th accident and N the total number of accidents incurred by the insurance company during a certain reference period (e.g. one year). Suppose that the amount of a loss is the sum of the claims related to the different coverages offered by a policy. These claims are most often correlated. The present paper aims to obtain bounds on the cumulative distribution function of S . These bounds can be derived when the marginal distributions of the claim amounts are specified or when only partial information is available.