Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/257943 
Year of Publication: 
2019
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 7 [Issue:] 4 [Article No.:] 105 [Publisher:] MDPI [Place:] Basel [Year:] 2019 [Pages:] 1-10
Publisher: 
MDPI, Basel
Abstract: 
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 μ/σ2 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).
Subjects: 
drawdown
linear diffusions
reflected Brownian motion
spectrally negative Lévy processes
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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