Boundary Crossing Problems for Compound Renewal Processes

[摘要] We find sharp asymptotics of the probability that the trajectory of a compound renewal process crosses (or does not cross) an arbitrary remote boundary. In particular, some limit theorems are obtained for the distribution of the maximum of the process in the domain of large deviations. We also give some applications to the classical ruin probability problem in insurance theory.

[学科分类] 数学（综合）

[关键词] compound renewal process;boundary crossing problems;large deviation;ruin probability problem