  We start by showing that the finite-time absolute ruin probability in the
classical risk model with constant interest force can be expressed in terms of
the transition probability of a positive Ornstein-Uhlenbeck type process, say
X. Our methodology applies to the case when the dynamics of the aggregate
claims process is a subordinator. From this expression, we easily deduce
necessary and sufficient conditions for the infinite-time absolute ruin to
occur. We proceed by showing that, under some technical conditions, the
transition density of X admits a spectral type representation involving merely
the limiting distribution of the process. As a by-product, we obtain a series
expansions for the finite-time absolute ruin probability. On the way, we also
derive, for the aforementioned risk process, the Laplace transform of the
first-exit time from an interval from above. Finally, we illustrate our results
by detailing some examples.
