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

Date

2020-06-01

Author

Vardar Acar, Ceren
Avram, Florin

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Path decomposition is performed to characterize the law of the pre-/post-supremum, post-infimum and the intermediate processes of a spectrally negative Levy 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.

URI

https://hdl.handle.net/11511/92329

Journal

Journal Of Theoretical Probability

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Department of Statistics, Article

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Maximum Drawdown and Drawdown Duration of Spectrally Negative Levy Processes Decomposed at Extremes Vardar Acar, Ceren; Avram, Florin (Springer Science and Business Media LLC, 2020-06-06) Path decomposition is performed to characterize the law of the pre-/post-supremum, post-infimum and the intermediate processes of a spectrally negative Levy 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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Maximum Loss and Maximum Gain of Spectrally Negative Levy Processes Vardar Acar, Ceren (2017-12-08) The joint distribution of the maximum loss and the maximum gain is obtained for a spectrally negative L´evy 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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Citation Formats

C. Vardar Acar and F. Avram, “Maximum Drawdown and Drawdown Duration of Spectrally Negative Levy Processes Decomposed at Extremes,” Journal Of Theoretical Probability, vol. 34, no. 3, pp. 1486–1505, 2020, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/92329.