  If a given aggregate process $S$ is a compound mixed renewal process under a
probability measure $P$, we provide a characterization of all probability
measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively
equivalent and $S$ is converted into a compound mixed Poisson process under
$Q$. This result extends earlier works of Delbaen & Haezendonck [2], Embrechts
& Meister [5], Lyberopoulos & Macheras [11], and of the authors [14].
Implications to the ruin problem and to the computation of premium calculation
principles in an insurance market possessing the property of no free lunch with
vanishing risk are also discussed.
