Ruin probabilities expressed in terms of storage processes

It is shown by a simple sample path argument that the ruin probabilities for a risk reserve process with premium rate p ( r ) depending on the reserve r and finite or infinite horizon are related in a simple way to the state probabilities of a compound Poisson dam with the same release rate p ( r ) at content r. In the infinite horizon case, this result has been established by Harrison and Resnick (1978), and in the finite horizon case with constant p it extends well-known relations to the M/G/ 1 virtual waiting time.