Maximum loss and maximum gain of spectrally negative Levy processes

2015/10/13 by Ceren Vardar-Acar, Acar, Ceren Vardar, Mine Çağlar +1
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #60G51 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1510.03629

openalex publication_date 2015/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The joint distribution of the maximum loss and the maximum gain is obtained for a spectrally negative Levy 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.Keywords Maximum drawdown Maximum drawup Spectrally negative Reflected process Fluctuation theory

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