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If a given aggregate process $S$ is a compound mixed renewal process under aprobability measure $P$, we provide a characterization of all probabilitymeasures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressivelyequivalent 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 calculationprinciples in an insurance market possessing the property of no free lunch withvanishing risk are also discussed.

A characterization of equivalent martingale probability measures in a mixed renewal risk model with applications in Risk Theory