Uniform Asymptotics of Ruin Probabilities for Levy Processes

#### F. Avram, M. Kelbert, I. Sazonov

2012, v.18, №4, 681-692

ABSTRACT

In this paper we obtain, for spectrally negative Levy processes $X$, uniform approximations for the finite time ruin probability $\Psi(t,u) = {\mathbb P}_u[T\leq t],\quad T=\inf\{t\geq 0: X(t) < 0\},$ when $u=X(0)$ and $t$ tend to infinity such that $v=u/t$ is constant, and the so-called Cramer light-tail condition is satisfied.

Keywords: ruin probability,Cramer - Lundberg model,Levy process,Cremona equation,Saddle-point approximation,Fresnel integral