Maximum Loss and Maximum Gain of Spectrally Negative Levy Processes

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2017-12-08

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Vardar Acar, Ceren

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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.

Subject Keywords

Statistics and Probability, Engineering (miscellaneous), Economics, Econometrics and Finance (miscellaneous)

URI

https://hdl.handle.net/11511/38014

DOI

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

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Department of Statistics, Conference / Seminar

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Maximum loss and maximum gain of spectrally negative Levy processes Vardar Acar, Ceren (2017-12-13) 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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Maximum Drawdown and Drawdown Duration of Spectrally Negative Levy Processes Decomposed at Extremes Vardar Acar, Ceren; Avram, Florin (2020-06-01) 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.

Citation Formats

C. Vardar Acar, “Maximum Loss and Maximum Gain of Spectrally Negative Levy Processes,” 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38014.