Bounds for classical ruin probabilities

Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model

“…derived originally in De Vylder and Goovaerts (1984). Note that a general lower bound for ψ(x) which is a refinement of (14), has been given recently by Chadjiconstantinidis and Politis (2005); various other, both upper and lower, bounds for ψ(x), are given in that paper.…”

Two-Sided Bounds for Ruin Probabilities when the Adjustment Coefficient does not Exist

“…The upper bound is tighter than that of Dickson (1994). The corresponding lower bound, which holds under the same conditions, is tighter than that of De Vylder & Goovaerts (1984). Even when the adjustment coefficient exists, the upper bound is, in some cases, tighter than Lundberg's bound.…”

“…One method is to derive general bounds for the ruin probability (x) without the Cramér-Lundberg condition or other conditions similar to it, see, for example, De Vylder & Goovaerts (1984), Broeckx et al (1986).…”

Tail bounds for the distribution of the deficit in the renewal risk model

“…This bound was originally proved by De Vylder and Goovaerts (1984). By Willmot (2002, Theorem 3.2), we know that if the ladder height d.f.…”