Finite-horizon ruin probability asymptotics in the compound discrete-time risk model

In this paper, we consider the compound discrete-time risk model which is a modification of the classical discrete-time (compound binomial) risk model. In this model, the claims in each fixed subsequent time interval arrive independently, and their number is random. We find the asymptotics of finite-horizon ruin probability in such a model for a subclass of heavy-tailed claim sizes and claim numbers.