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

DOI10.1016/J.SPL.2009.04.014zbMath1175.60021arXiv0804.3169OpenAlexW2088145016MaRDI QIDQ840787

Zbigniew Palmowski, Martijn R. Pistorius

Publication date: 14 September 2009

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.3169

zbMATH Keywords

boundary crossingLévy processfirst passageCramér asymptoticsembedded random walkHöglund's renewal theorem

Mathematics Subject Classification ID

Large deviations (60F10) Renewal theory (60K05)

Related Items (7)

On future drawdowns of Lévy processes ⋮ Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes ⋮ Ruin probabilities for risk process in a regime-switching environment ⋮ Ruin probabilities in classical risk models with gamma claims ⋮ The exact asymptotics for hitting probability of a remote orthant by a multivariate Lévy process: the Cramér case ⋮ A note on first passage probabilities of a L\'evy process reflected at a general barrier ⋮ Optimal control and dependence modeling of insurance portfolios with Lévy dynamics

Cites Work

• Hitting probabilities and large deviations
• An asymptotic expression for the probability of ruin within finite time
• Sequential analysis. Tests and confidence intervals
• Cramér's estimate for Lévy processes
• Ruin probabilities expressed in terms of ladder height distributions
• Pricing Barrier Options with Time–Dependent Coefficients
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