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A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts. (English) Zbl 1231.91152
Summary: 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.

MSC:
91B30 Risk theory, insurance (MSC2010)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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