EXACT AND ASYMPTOTIC SOLUTIONS FOR THE TIME-DEPENDENT PROBLEM OF COLLECTIVE RUIN .2.

We consider a model for the risk reserve Z(t) of an insurance company. It is assumed that Z(t) increases due to premium intake and also as t he reserve earns interest. The reserve decreases due to claims, which are modeled as a compound Poisson process. Previously [SIAM J. Appl. M ath., 54 (1994), pp. 1745-1767] we obtained an integral representation for the probability that Z(t) remains positive through time t, which is also the probability that the company survives up to this time. We now study asymptotic properties of this probability. It is assumed tha t the rate at which the reserve earns interest is small (but nonzero).