Cramér asymptotics for finite time first passage probabilities of general Lévy processes

Zbigniew Palmowski , Martijn Pistorius

We derive the exact asymptotics of if and tend to infinity with constant, for a general Lévy process that admits exponential moments. The proof is based on a renewal argument and a two-dimensional renewal theorem of Höglund [Höglund, T., 1990. An asymptotic expression for the probability of ruin within finite time. Ann. Prob., 18, 378–389].

Mots clés: Physical Sciences

Zbigniew Palmowski, Martijn Pistorius. Cramér asymptotics for finite time first passage probabilities of general Lévy processes. Statistics and Probability Letters, 2009, 79 (16), pp.1752. ⟨10.1016/j.spl.2009.04.014⟩. ⟨hal-00558699⟩