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Impact of dependence among multiple claims in a single loss. (English) Zbl 1103.91357

Summary: In the collective risk model, the aggregate claim amount for the portfolio is denoted by \(S=X_1+X_2+\dots +X_N\) where \(X_i\), \(i\geq 1\), 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
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