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Three Essays on Stopping

Author

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  • Eberhard Mayerhofer

    (Department of Mathematics and Statistics, University of Limerick, Limerick V94TP9X, Ireland)

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 / σ 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 Lévy process, a result due to Mijatović and Pistorius (2012). Our proof is similar, but simpler than Lehoczky (1977) or Landriault et al. (2017).

Suggested Citation

  • Eberhard Mayerhofer, 2019. "Three Essays on Stopping," Risks, MDPI, vol. 7(4), pages 1-10, October.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:4:p:105-:d:278018
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    References listed on IDEAS

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    1. Golub, Anton & Chliamovitch, Gregor & Dupuis, Alexandre & Chopard, Bastien, 2016. "Multi-scale representation of high frequency market liquidity," Algorithmic Finance, IOS Press, vol. 5(1-2), pages 3-19.
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    Cited by:

    1. James B. Glattfelder & Anton Golub, 2022. "Bridging the Gap: Decoding the Intrinsic Nature of Time in Market Data," Papers 2204.02682, arXiv.org.

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