Second order tail approximation for the maxima of randomly weighted sums with applications to ruin theory and numerical examples

In this paper the second order asymptotics for the tail probability of the maxima of randomly weighted sums is established under the assumption that the underlying primary random variables have a regularly varying density as x tends to infinity. In doing so, some mild conditions are imposed on the tails of the random weights, and no any assumption is made on the dependence structure between these weights. What is more, an application to insurance risk theory is presented and some numerical examples are given to show the accuracy of the second order results. (C) 2019 Published by Elsevier B.V.