Large deviations of aggregate amount of claims in compound risk model with arbitrary dependence between claim sizes and waiting times

In this paper, we consider a nonstandard compound renewal risk model with arbitrary dependence between the aggregate amount of claims caused by an accident and the waiting time of the corresponding accident. For the case when various dependence structures are imposed among the involved modeling factors and the common claim-size distribution is consistently varying tailed, we obtain for the large deviations of the aggregate amount of claims some asymptotic results, which hold uniformly for all x in a t-interval.