On Randomized Reinsurance Contracts

Abstract

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.

Keywords: optimal reinsurance, randomization, stop-loss treaties, cost of capital, mean-excess function

JEL Classification: G22, C61