Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions

Equilibrium distributions arise naturally in ruin theory and may be characterized in terms of the mean residual lifetime, an analytic and statistical tool for analyzing insurance claim size distributions. Bounds for the right tail of the total claim distribution which refine and generalize previous results are constructed which depend on properties of the equilibrium distribution of the claim size distribution and the mean residual lifetime in particular. Moment based Pareto bounds are considered in some detail. Extensions are considered to higher-order equilibrium distributions.