In this talk, we study asymptotic tail behavior ofa randomly stopped Lévy process and its maximum over random timeinterval. For various cases, under the assumption that either the Lévy measureor the random stopping time has a heavy right tail we derive exact asymptotic expressions for their taildistributions. The main methods consist of decomposition of Lévy process, probability inequalities forLévy process, and properties of heavy-tailed distribution.
