Maximum loss and maximum gain of spectrally negative Levy processes

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