On the Optimality of Multiline Excess of Loss Covers

It is well known that diversifying the risk between independent policies reduces the total risk in the sense that less deviations around the aggregate mean loss are expected. In other words, less capital has to be allocated due to the diversification effect. The same effect can be obtained when an insurance company buys an excess of loss cover. Instead of buying independently covers for different lines of business, it is intuitively acceptable to believe that the insurance company has interest in diversifying by buying a multiline excess of loss cover. In the present paper I show how to deal with the dependencies induced by such a model and using some risk measures we show on a numerical example the optimality of the multiline agreement.