Other Topics

Abstract

In this chapter various related topics are briefly discussed. In Sect. 8.1 ruin-based quantities are considered, including the ‘surplus immediately after the second last claim before ruin’; the minimum surplus before ruin; and the discounted aggregate claims until ruin and the number of claims until ruin. It is worth mentioning that expressions obtained for the marginal density of the time of ruin are typically infinite series expansions, and the individual terms may often be interpreted in terms of the joint distribution of the time of ruin and the number of claims until ruin. Section 8.2 considers ordering properties involving various ruin-based quantities, giving results which agree with intuition. Finally, Sect. 8.3 derives various Lundberg type bounds on the solution of renewal equations, the latter of which appear repeatedly throughout the monograph.