Maximum loss and maximum gain of spectrally negative Lévy processes

Abstract

The joint distribution of the maximum loss and the maximum gain is obtained for a spectrally negative Lévy process until the passage time of a given level. Their marginal distributions up to an independent exponential time are also provided. The existing formulas for Brownian motion with drift are recovered using the particular scale functions.

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Correspondence to Ceren Vardar-Acar.

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This work is supported by the Scientific and Technological Research Council of Turkey, TUBITAK Project No.110T674

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Vardar-Acar, C., Çağlar, M. Maximum loss and maximum gain of spectrally negative Lévy processes. Extremes 20, 301–308 (2017). https://doi.org/10.1007/s10687-016-0279-8

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Keywords

  • Maximum drawdown
  • Maximum drawup
  • Spectrally negative
  • Reflected process
  • Fluctuation theory

AMS 2000 Subject Classifications

  • 60G17
  • 60G70
  • 60G35