Precise large deviation of claim surplus process in a renewal risk model with random premium income

摘要

In this paper, we consider a nonstandard renewal risk model in which claim sizes and corresponding inter-arrival times form a sequence of independent and identically distributed random pairs. Each pair satisfies a certain dependence structure. In addition, premium income is described by a compound Poisson process. When the distribution of claim sizes belongs to the consistent variation class, we obtain precise large deviation of claim surplus process.