  Generalizing earlier works of Delbaen & Haezendonck [5] as well as of [18]
and [16] for given compound mixed renewal process S under a probability measure
P, we characterize all those probability measures Q on the domain of P such
that Q and P are progressively equivalent and S remains a compound mixed
renewal process under Q with improved properties. As a consequence, we prove
that any compound mixed renewal process can be converted into a compound mixed
Poisson process through a change of measures. Applications related to the ruin
problem and to the computation of premium calculation principles in an
insurance market without arbitrage opportunities are discussed in [26] and
[27], respectively.
