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Maximum loss and maximum gain of spectrally negative Lévy processes

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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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Authors and Affiliations

  1. Department of Statistics, Middle East Technical University, Ankara, Turkey

    Ceren Vardar-Acar

  2. Department of Mathematics, Koç University, Istanbul, Turkey

    Mine Çağlar

Authors
  1. Ceren Vardar-Acar
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  2. Mine Çağlar
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Corresponding author

Correspondence to Ceren Vardar-Acar.

Additional information

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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  • DOI: https://doi.org/10.1007/s10687-016-0279-8

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