A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts

In this paper a purely theoretical reinsurance model is presented, where the reinsurance contract is assumed to be simultaneously of an excess of loss and of a proportional type. The stochastic structure of the set of pairs (claim’s arrival time, claim’s size) is described by a Spatial Mixed Poisson Process. By using an invariance property of the Spatial Mixed Poisson Processes, we estimate the amount that the ceding company obtains in a fixed time interval in force of the reinsurance contract.