Mayerhofer_2019_Three.pdf (363.1 kB)
Three essays on stopping
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 m/s2 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 Lévy process, a result due to Mijatovi´c and Pistorius (2012). Our proof is similar, but simpler than Lehoczky (1977) or Landriault et al. (2017).
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