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

Asymptotic aspects of the Gerber–Shiu function in the renewal risk model using Wiener–Hopf factorization and convolution equivalence

“…Very often it is impossible to get closed-form formulas, or the established integro-differential equations are not solvable at all, or the calculation is rather involved. For bounds, we refer to Ng and Yang (2005), Psarrakos and Politis (2008), and Psarrakos (2008).…”

Bounds for the Ruin Probability in the Sparre–Andersen Model

“…Proof. By Psarrakos (2008), we know that if the labber height d.f. F is NWU (NBU) then a lower (upper) bound for the tail of the deficit H(u, y) is…”