  If a given aggregate process $S$ is a compound mixed Poisson process under a
probability measure $P$, a characterization of all probability measures $Q$ on
the domain of $P$, such that $P$ and $Q$ are progressively equivalent and $S$
remains a compound mixed Poisson process with improved properties, is provided.
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.
