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Teoriya Veroyatnostei i ee Primeneniya, 1999, Volume 44, Issue 1, Pages 3–13
DOI: https://doi.org/10.4213/tvp594
(Mi tvp594)
 

This article is cited in 48 scientific papers (total in 48 papers)

On probability characteristics of “downfalls” in a standard Brownian motion

R. Douady, M. Yora, A. N. Shiryaevb

a Laboratoire de Probabilités, Université Paris VI, France
b Steklov Mathematical Institute, Russian Academy of Sciences
Abstract: For a Brownian motion B=(Bt)t1 with B0=0, EBt=0, EB2t=t problems of probability distributions and their characteristics are considered for the variables
D=sup
where \sigma and \sigma' are times (non-Markov) of the absolute maximum and absolute minimum of the Brownian motion on [0,1] (i.e., B_\sigma=\sup_{0\le t\le 1}B_t, B_{\sigma'}=\inf_{0\le t'\le 1}B_{t'}).
Keywords: Brownian motion, “downfalls” and “range”, Lévy theorem, Brownian meander.
Received: 24.08.1998
English version:
Theory of Probability and its Applications, 2000, Volume 44, Issue 1, Pages 29–38
DOI: https://doi.org/10.1137/S0040585X97977306
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: R. Douady, M. Yor, A. N. Shiryaev, “On probability characteristics of “downfalls” in a standard Brownian motion”, Teor. Veroyatnost. i Primenen., 44:1 (1999), 3–13; Theory Probab. Appl., 44:1 (2000), 29–38
Citation in format AMSBIB
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\paper On probability characteristics of ``downfalls'' in a standard Brownian motion
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\pages 3--13
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\zmath{https://zbmath.org/?q=an:0959.60073}
\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 44
\issue 1
\pages 29--38
\crossref{https://doi.org/10.1137/S0040585X97977306}
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Linking options:
  • https://www.mathnet.ru/eng/tvp594
  • https://doi.org/10.4213/tvp594
  • https://www.mathnet.ru/eng/tvp/v44/i1/p3
  • This publication is cited in the following 48 articles:
    1. Yifan Li, “On the Brownian range and the Brownian reversal”, J. Appl. Probab., 2024, 1  crossref
    2. M. Salcı‐Bilici, F. P{\i}nar Erdem, İbrahim Ünalmış, C. Vardar‐Acar, “Has the Last Super Cycle in Crude Oil Price Ended? a Maximum Drawdown Approach Using Fractional Brownian Motion”, Appl Stoch Models Bus & Ind, 2024  crossref
    3. Gongqiu Zhang, Lingfei Li, “A general method for analysis and valuation of drawdown risk”, Journal of Economic Dynamics and Control, 152 (2023), 104669  crossref
    4. Brinker L.V., “Minimal Expected Time in Drawdown Through Investment For An Insurance Diffusion Model”, Risks, 9:1 (2021), 17  crossref  isi
    5. Zhang X., Li L., Zhang G., “Pricing American Drawdown Options Under Markov Models”, Eur. J. Oper. Res., 293:3 (2021), 1188–1205  crossref  isi
    6. Gongqiu Zhang, Lingfei Li, “A General Method for Analysis and Valuation of Drawdown Risk under Markov Models”, SSRN Journal, 2021  crossref
    7. Van Hemert O., Ganz M., Harvey C.R., Rattray S., Martin E.S., Yawitch D., “Drawdowns”, J. Portf. Manage., 46:8 (2020), 34–50  crossref  isi
    8. Otto van Hemert, Mark Ganz, Campbell R. Harvey, Sandy Rattray, Eva Sanchez Martin, Darrel Yawitch, “Drawdowns”, SSRN Journal, 2020  crossref
    9. Bai L., Liu P., “Drawdown and Drawup For Fractional Brownian Motion With Trend”, J. Theor. Probab., 32:3 (2019), 1581–1612  crossref  isi
    10. Dassios A., Lim J.W., “A Variation of the Azema Martingale and Drawdown Options”, Math. Financ., 29:4 (2019), 1116–1130  crossref  isi
    11. Gapeev V P., Rodosthenous N., Chinthalapati V.L.R., “On the Laplace Transforms of the First Hitting Times For Drawdowns and Drawups of Diffusion-Type Processes”, Risks, 7:3 (2019), 87  crossref  isi
    12. Muneer Shaik, S. Maheswaran, “Robust Volatility Estimation with and Without the Drift Parameter”, J. Quant. Econ., 17:1 (2019), 57  crossref
    13. Cui Zh., Duy Nguyen, “Magnitude and Speed of Consecutive Market Crashes in a Diffusion Model”, Methodol. Comput. Appl. Probab., 20:1 (2018), 117–135  crossref  mathscinet  zmath  isi  scopus
    14. Dassios A., Lim J.W., “An Efficient Algorithm For Simulating the Drawdown Stopping Time and the Running Maximum of a Brownian Motion”, Methodol. Comput. Appl. Probab., 20:1 (2018), 189–204  crossref  mathscinet  zmath  isi  scopus
    15. van den Berg M., den Hollander F., “Torsional Rigidity For Cylinders With a Brownian Fracture”, Bull. London Math. Soc., 50:2 (2018), 321–339  crossref  zmath  isi  scopus
    16. Mahmoud O., “The temporal dimension of risk”, J. Risk, 19:3 (2017), 57–83  crossref  mathscinet  isi  scopus
    17. Landriault D., Li B., Zhang H., “On magnitude, asymptotics and duration of drawdowns for Lévy models”, Bernoulli, 23:1 (2017), 432–458  crossref  mathscinet  zmath  isi  elib  scopus
    18. Goldberg L.R., Mahmoud O., “Drawdown: From Practice to Theory and Back Again”, Math. Financ. Econ., 11:3 (2017), 275–297  crossref  mathscinet  zmath  isi  scopus
    19. Molyboga M., L'Ahelec Ch., “Portfolio Management With Drawdown-Based Measures”, J. Altern. Invest., 19:3 (2017), 75–89  crossref  isi  scopus
    20. Landriault D., Li B., Zhang H., “A Unified Approach For Drawdown (Drawup) of Time-Homogeneous Markov Processes”, J. Appl. Probab., 54:2 (2017), 603–626  crossref  mathscinet  isi  scopus
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