A characterization of martingale-equivalent mixed compound Poisson processes

Abstract

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 & Haezendonck (1989). 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.