## 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)

### Keywords:

Stochastic dominance; Dependence; Collective risk model
Full Text:

### References:

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