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Stochastics and Stochastic Reports Volume 75, 2003 - Issue 4
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Original Articles

Optimal prediction of the ultimate maximum of Brownian motion

Jesper Lund PedersenCorrespondence[email protected]
Pages 205-219 | Accepted 21 Mar 2003, Published online: 17 Oct 2011

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B. Jensen & J. L. Pedersen. (2007) A digitalized employee option. Stochastics 79:1-2, pages 103-115.
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Articles from other publishers (36)

Tomasz Kosmala, Randall Martyr & John Moriarty. (2022) Markov risk mappings and risk-sensitive optimal prediction. Mathematical Methods of Operations Research 97:1, pages 91-116.
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Tiziano De Angelis. (2022) Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon. Electronic Journal of Probability 27:none.
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Yulin Song & Yingchao Xie. (2017) Existence of Density Functions for the Running Maximum of a Lévy-Itô Diffusion. Potential Analysis 48:1, pages 35-48.
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Dmitry B. Rokhlin. (2016) Minimax perfect stopping rules for selling an asset near its ultimate maximum. Optimization Letters 11:8, pages 1743-1756.
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A. A. Kamenov. (2015) Optimal stopping for absolute maximum of homogeneous diffusion. Moscow University Mathematics Bulletin 70:5, pages 202-207.
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Goran Peskir. (2014) Quickest detection of a hidden target and extremal surfaces. The Annals of Applied Probability 24:6.
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Nick H. Bingham & Goran Peskir. 2014. Wiley StatsRef: Statistics Reference Online. Wiley StatsRef: Statistics Reference Online.
Kristoffer Glover & Hardy Hulley. (2014) Optimal Prediction of the Last-Passage Time of a Transient Diffusion. SIAM Journal on Control and Optimization 52:6, pages 3833-3853.
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Kristoffer Glover, Hardy Hulley & Goran Peskir. (2013) Three-dimensional Brownian motion and the golden ratio rule. The Annals of Applied Probability 23:3.
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S. C. P. Yam, S. P. Yung & W. Zhou. (2013) A Unified “Bang-Bang” Principle with Respect to ${\ccR}$-Invariant Performance Benchmarks. Theory of Probability & Its Applications 57:2, pages 357-366.
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Pieter C. Allaart. (2016) Predicting the Supremum: Optimality of ‘Stop at Once or Not at All’. Journal of Applied Probability 49:3, pages 806-820.
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Pieter C. Allaart. (2016) Predicting the Supremum: Optimality of ‘Stop at Once or Not at All’. Journal of Applied Probability 49:03, pages 806-820.
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S. C. P. Yam, S. P. Yung & W. Zhou. (2012) Optimal selling time in stock market over a finite time horizon. Acta Mathematicae Applicatae Sinica, English Series 28:3, pages 557-570.
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Goran Peskir. (2012) Optimal detection of a hidden target: The median rule. Stochastic Processes and their Applications 122:5, pages 2249-2263.
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S C. P. Yam, S C. P. Yam, S P Yung, S P Yung, W Zhou & W Zhou. (2012) A unified “bang-bang” principle with respect to R-invariant performance benchmarksA unified “bang-bang” principle with respect to R-invariant performance benchmarks. Теория вероятностей и ее применения Teoriya Veroyatnostei i ee Primeneniya 57:2, pages 405-414.
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Katsunori Ano & Roman Ivanov. (2012) On predicting the ultimate maximum for exponential Lévy processes. Electronic Communications in Probability 17:none.
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S. S. Sinelnikov. (2012) On the Optimal Stopping of a Brownian Motion with a Negative Drift. Theory of Probability & Its Applications 56:2, pages 343-350.
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Min Dai, Zhou Yang & Yifei Zhong. (2012) Optimal Stock Selling Based on the Global Maximum. SIAM Journal on Control and Optimization 50:4, pages 1804-1822.
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Gilles-Edouard Espinosa & Nizar Touzi. (2012) Detecting the Maximum of a Scalar Diffusion with Negative Drift. SIAM Journal on Control and Optimization 50:5, pages 2543-2572.
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Min Dai & Yifei Zhong. (2010) OPTIMAL STOCK SELLING/BUYING STRATEGY WITH REFERENCE TO THE ULTIMATE AVERAGE. Mathematical Finance 22:1, pages 165-184.
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Violetta Bernyk, Robert C. Dalang & Goran Peskir. (2011) Predicting the ultimate supremum of a stable Lévy process with no negative jumps. The Annals of Probability 39:6.
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S. S. Sinelnikov. (2011) The optimal stopping problem concerned with ultimate maximum of a Lévy process. Moscow University Mathematics Bulletin 66:4, pages 158-162.
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Сергей Сергеевич Синельников & Sergey Sergeevich Sinelnikov. (2011) Об оптимальной остановке броуновского движения с отрицательным сносомOn optimal stopping for Brownian motion with a negative drift. Теория вероятностей и ее применения Teoriya Veroyatnostei i ee Primeneniya 56:2, pages 391-398.
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Pieter Allaart. (2016) A General ‘Bang-Bang’ Principle for Predicting the Maximum of a Random Walk. Journal of Applied Probability 47:4, pages 1072-1083.
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Pieter Allaart. (2016) A General ‘Bang-Bang’ Principle for Predicting the Maximum of a Random Walk. Journal of Applied Probability 47:04, pages 1072-1083.
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Jacques du Toit & Goran Peskir. (2009) Selling a stock at the ultimate maximum. The Annals of Applied Probability 19:3.
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A. N. Shiryaev. (2009) On Conditional-Extremal Problems of the Quickest Detection of Nonpredictable Times of the Observable Brownian Motion. Theory of Probability & Its Applications 53:4, pages 663-678.
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Nick H. Bingham & Goran Peskir. 2007. Encyclopedia of Quantitative Risk Analysis and Assessment. Encyclopedia of Quantitative Risk Analysis and Assessment.
Альберт Николаевич Ширяев & Albert Nikolaevich Shiryaev. (2008) Об условно-экстремальных задачах скорейшего обнаружения непредсказуемых моментов у наблюдаемого броуновского движенияOn Conditional-Extremal Problems of the Quickest Detection of Nonpredictable Times of the Observable Brownian Motion. Теория вероятностей и ее применения Teoriya Veroyatnostei i ee Primeneniya 53:4, pages 751-768.
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Jacques du Toit & Goran Peskir. 2008. Mathematical Control Theory and Finance. Mathematical Control Theory and Finance 95 112 .
J. du Toit & G. Peskir. (2007) The trap of complacency in predicting the maximum. The Annals of Probability 35:1.
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Goran Peskir. (2006) On Reflecting Brownian Motion with Drift. Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2006:0, pages 1-5.
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Jesper Lund Pedersen. 2005. Recent Advances in Applied Probability. Recent Advances in Applied Probability 427 454 .
Jan Obłój. (2004) The Skorokhod embedding problem and its offspring. Probability Surveys 1:none.
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Min Dai, Zhou Yang & Yifei Zhong. (2012) Optimal Stock Selling Based on the Global Maximum. SSRN Electronic Journal.
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Min Dai & Yifei Zhong. (2008) Optimal Stock Selling/Buying Strategy with Reference to the Ultimate Average. SSRN Electronic Journal.
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