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

Zbigniew Palmowski and Martijn Pistorius

Statistics & Probability Letters, 2009, vol. 79, issue 16, 1752-1758

Abstract: We derive the exact asymptotics of P(supu x) if x and t tend to infinity with x/t constant, for a general Lévy process X 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].

Date: 2009
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