Large-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilities

Abstract

We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of i.i.d. standard uniform random variables. This extends a corresponding result of Korshunov. As an application, we generalize a result of Tang, the uniform asymptotic estimate for the finite-time ruin probability, to the whole strongly subexponential class.