Estimating tails of independently stopped random walks using concave approximations of hazard functions

Abstract This paper considers logarithmic asymptotics of tails randomly stopped sums. The stopping is assumed to be independent the underlying random walk. First, finiteness ordinary moments revisited. Then study expanded more general asymptotic analysis. Results are applicable a large class heavy-tailed variables. main result enables one identify if behaviour sum dominated by its increments or variable. As consequence, new sufficient conditions for moment determinacy compounded sums obtained.