A CHARACTERIZATION OF MARTINGALE-EQUIVALENT MIXED COMPOUND POISSON PROCESSES

If a given aggregate process S is a mixed compound Poisson process under a probability measure P, we provide a characterization of all probability measures Q on the domain of P, such that P and Q are progressively equivalent and S remains a mixed compound Poisson process with improved properties. This result generalizes earlier work of Delbaen and Haezendonck (Insurance Math. Econom. 8 (1989) 269-277). Implications related to the computation of premium calculation principles in an insurance market possessing the property of no free lunch with vanishing risk are also discussed.

Automated summary

This study investigates mixed compound Poisson processes under a probability measure, providing a characterization of all probability measures to maintain equivalence while improving the properties of the process. The research also discusses implications for premium calculation principles in an insurance market without free lunch and vanishing risk.