The Effect of Excess-of-Loss Reinsurance with Reinstatements of the Cedent's Portfolio.

The adjustment for the cedent's retained risk after excess-of-loss reinsurance with reinstatements is calculated. Therefore we need a multivariate aggregate claims distribution. This distribution is easily given by a multivariate extension of Panjer's recursion. Numerical examples show the interest for the cedent to calculate the adjustment coeeficient for its portfolio when buying excess of loss reinsurance with reinstatements. An optimal organization is discussed.