Maximum loss and maximum gain of spectrally negative Levy processes

Date

2017-12-13

Author

Vardar Acar, Ceren

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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.

Subject Keywords

Maximum drawdown, Maximum drawup, Spectrally negative, Reflected process, Fluctuation theory

URI

https://link.springer.com/article/10.1007/s10687-016-0279-8
https://hdl.handle.net/11511/71237

Journal

Extremes

Collections

Department of Statistics, Article

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Maximum Loss of Spectrally Negative Lévy Processes Vardar Acar, Ceren (null; 2018-06-21) The joint distribution of the maximum loss and the maximum gain is obtained for a spectrally negative L,vy 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.
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.
Distribution of maximum loss of fractional Brownian motion with drift Vardar Acar, Ceren (2013-07-04) In this paper, we find bounds on the distribution of the maximum loss of fractional Brownian motion H ≥ 1/2 with and derive estimates on its tail probability. Asymptotically, the tail of the distribution of maximum loss over [0, t] behaves like the tail of the marginal distribution at time . t
Distribution of maximum loss of fractional Brownian motion with drift Caglar, Mine; Vardar Acar, Ceren (Elsevier BV, 2013-12) In this paper, we find bounds on the distribution of the maximum loss of fractional Brownian motion with H >= 1/2 and derive estimates on its tail probability. Asymptotically, the tail of the distribution of maximum loss over [0, t] behaves like the tail of the marginal distribution at time t.
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.

Citation Formats

C. Vardar Acar, “Maximum loss and maximum gain of spectrally negative Levy processes,” Extremes, pp. 301–308, 2017, Accessed: 00, 2021. [Online]. Available: https://link.springer.com/article/10.1007/s10687-016-0279-8.