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Maximum Drawdown and Drawdown Duration of Spectrally Negative Lévy Processes Decomposed at Extremes

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Abstract

Path decomposition is performed to characterize the law of the pre-/post-supremum, post-infimum and the intermediate processes of a spectrally negative Lévy process taken up to an independent exponential time T. As a result, mainly the distributions of the supremum of the post-infimum process and the maximum drawdown of the pre-/post-supremum, post-infimum processes and the intermediate processes are obtained together with the law of drawdown durations.

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Acknowledgements

We are grateful to Andreas E. Kyprianou for helpful discussions on the post-infimum process.

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Authors and Affiliations

  1. Middle East Technical University, Ankara, Turkey

    Ceren Vardar-Acar

  2. Koc University, Istanbul, Turkey

    Mine Çağlar

  3. Universite de Pau, Pau, France

    Florin Avram

Authors
  1. Ceren Vardar-Acar
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  2. Mine Çağlar
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  3. Florin Avram
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Correspondence to Ceren Vardar-Acar.

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This work is supported by Tübitak Project with number 117F273.

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Vardar-Acar, C., Çağlar, M. & Avram, F. Maximum Drawdown and Drawdown Duration of Spectrally Negative Lévy Processes Decomposed at Extremes. J Theor Probab 34, 1486–1505 (2021). https://doi.org/10.1007/s10959-020-01014-z

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  • DOI: https://doi.org/10.1007/s10959-020-01014-z

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