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

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 t...

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Bibliographic Details
Published in:Journal of theoretical probability 2021-09, Vol.34 (3), p.1486-1505
Main Authors: Vardar-Acar, Ceren, Çağlar, Mine, Avram, Florin
Format: Article
Language:English
Subjects:
Decomposition
Infimum
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
Stochastic processes
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Summary: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.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-020-01014-z