Optimal prediction of the ultimate maximum of Brownian motion

DOI10.1080/1045112031000118994zbMath1032.60038OpenAlexW2051389913MaRDI QIDQ4440446

Jesper Lund Pedersen

Publication date: 18 December 2003

Published in: Stochastics and Stochastic Reports (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/1045112031000118994

zbMATH Keywords

viscosity solutionoptimal stoppingBrownian motionultimate maximumLévy's distributional theoremsmooth fit (at a single point)

Mathematics Subject Classification ID

Brownian motion (60J65) Stopping times; optimal stopping problems; gambling theory (60G40) Diffusion processes (60J60)

Related Items (16)

Predicting the Supremum: Optimality of ‘Stop at Once or Not at All’ ⋮ Selling a stock at the ultimate maximum ⋮ The trap of complacency in predicting the maximum ⋮ Minimax perfect stopping rules for selling an asset near its ultimate maximum ⋮ Existence of density functions for the running maximum of a Lévy-Itô diffusion ⋮ Optimal detection of a hidden target: the median rule ⋮ Three-dimensional Brownian motion and the golden ratio rule ⋮ Markov risk mappings and risk-sensitive optimal prediction ⋮ Predicting the ultimate supremum of a stable Lévy process with no negative jumps ⋮ Quickest detection of a hidden target and extremal surfaces ⋮ OPTIMAL STOCK SELLING/BUYING STRATEGY WITH REFERENCE TO THE ULTIMATE AVERAGE ⋮ Optimal selling time in stock market over a finite time horizon ⋮ A General ‘Bang-Bang’ Principle for Predicting the Maximum of a Random Walk ⋮ The optimal stopping problem concerned with ultimate maximum of a Lévy process ⋮ Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon ⋮ Optimal stopping for absolute maximum of homogeneous diffusion

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