On randomized reinsurance contracts

In this paper we discuss the potential of randomizing reinsurance treaties for efficient risk management. While it may be considered counter-intuitive to introduce additional external randomness in the determination of the retention function for a given occurred loss, we indicate why and to what extent randomizing a treaty can be interesting for the insurer. We illustrate the approach with a detailed analysis of the effects of randomizing a stop-loss treaty on the expected pro t after reinsurance in the framework of a one-year reinsurance model under regulatory solvency constraints and cost of capital considerations