%0 Journal Article
%T Three Essays on Stopping
%J Risks | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/risks7040105
%X First, we give a closed-form formula for first passage time of a reflected Brownian motion with drift. This corrects a formula by Perry et al. (2004). Second, we show that the maximum before a fixed drawdown is exponentially distributed for any drawdown, if and only if the diffusion characteristic ¦Ì / ¦Ò 2 is constant. This complements the sufficient condition formulated by Lehoczky (1977). Third, we give an alternative proof for the fact that the maximum before a fixed drawdown is exponentially distributed for any spectrally negative L¨¦vy process, a result due to Mijatovi£¿ and Pistorius (2012). Our proof is similar, but simpler than Lehoczky (1977) or Landriault et al. (2017). View Full-Tex
%U https://www.mdpi.com/2227-9091/7/4/105