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On the asymptotic behaviour of Lévy processes, Part I: Subexponential and exponential processes

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  • Albin, J.M.P.
  • Sundén, Mattias

Abstract

We study tail probabilities of the suprema of Lévy processes with subexponential or exponential marginal distributions over compact intervals. Several of the processes for which the asymptotics are studied here for the first time have recently become important to model financial time series. Hence our results should be important, for example, in the assessment of financial risk.

Suggested Citation

  • Albin, J.M.P. & Sundén, Mattias, 2009. "On the asymptotic behaviour of Lévy processes, Part I: Subexponential and exponential processes," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 281-304, January.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:1:p:281-304
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    References listed on IDEAS

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    1. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
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    5. Braverman, Michael, 2000. "Suprema of compound Poisson processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 145-156, November.
    6. Willekens, Eric, 1987. "On the supremum of an infinitely divisible process," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 173-175.
    7. Braverman, Michael, 2005. "On a class of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 179-189, December.
    8. Braverman, Michael & Samorodnitsky, Gennady, 1995. "Functionals of infinitely divisible stochastic processes with exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 207-231, April.
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    1. Braverman, Michael, 2010. "On suprema of Lévy processes with light tails," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 541-573, April.
    2. Saulius Paukštys & Jonas Šiaulys & Remigijus Leipus, 2023. "Truncated Moments for Heavy-Tailed and Related Distribution Classes," Mathematics, MDPI, vol. 11(9), pages 1-15, May.

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