Three Essays on Stopping
Department of Mathematics and Statistics, University of Limerick, Limerick V94TP9X, Ireland
Risks 2019, 7(4), 105; https://doi.org/10.3390/risks7040105
Received: 27 September 2019 / Revised: 16 October 2019 / Accepted: 16 October 2019 / Published: 18 October 2019
(This article belongs to the Special Issue Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics)
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
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 Mijatović and Pistorius (2012). Our proof is similar, but simpler than Lehoczky (1977) or Landriault et al. (2017).
Keywords: reflected Brownian motion; linear diffusions; spectrally negative Lévy processes; drawdown
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Mayerhofer, E. Three Essays on Stopping. Risks 2019, 7, 105.
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Mayerhofer E. Three Essays on Stopping. Risks. 2019; 7(4):105.Chicago/Turabian Style
Mayerhofer, Eberhard. 2019. "Three Essays on Stopping." Risks 7, no. 4: 105.
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