Dependency of insurance risks and the Burr distribution

Recently, several authors in the actuarial literature have derived approximations for sums of random variables when the distributions of terms are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. The approximations obtained are bounds in the sense of convex order. In this paper, we first give an overview of the recent actuarial literature on this topic. Secondly, we derive convex lower and upper bounds for sums of Burr distributed random variables.