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In insurance, the compound Poisson process is commonly used to model risk. This process assumes independence between the counting process (Poisson process) and the claims (independent and identically distributed random variables), making the calculation of the first two cumulants straightforward. However, these assumptions limit the applicability of this model to certain types of risks. To address these limitations, we propose a similar model where the counting process is a Hawkes process, with its intensity being influenced by the occurrence of claims. To this end, we will present a general process that encompasses this problem but also allows us to imagine other applications.