Three-dimensional Brownian motion and the golden ratio rule

DOI10.1214/12-AAP859zbMath1408.60032arXiv1303.2891OpenAlexW2038224795MaRDI QIDQ1950257

Hardy Hulley, Kristoffer J. Glover, Goran Peskir

Publication date: 10 May 2013

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.2891

zbMATH Keywords

Bessel processBrownian motionoptimal predictionbubblestransient diffusiongolden ratioconstant elasticity of variance modelstrict local martingalemaximality principleFibonacci retracementsupport and resistance levels

Mathematics Subject Classification ID

Variational inequalities (49J40) Brownian motion (60J65) Nonlinear ordinary differential equations and systems (34A34) Stopping times; optimal stopping problems; gambling theory (60G40) Martingales with continuous parameter (60G44) Diffusion processes (60J60)

Related Items (15)

Perpetual American options in diffusion-type models with running maxima and drawdowns ⋮ Perpetual American double lookback options on drawdowns and drawups with floating strikes ⋮ Optimal double stopping problems for maxima and minima of geometric Brownian motions ⋮ Optimal stopping problems for maxima and minima in models with asymmetric information ⋮ Optimal prediction of resistance and support levels ⋮ Perpetual American Standard and Lookback Options with Event Risk and Asymmetric Information ⋮ On the drawdowns and drawups in diffusion-type models with running maxima and minima ⋮ Predicting the last zero before an exponential time of a spectrally negative Lévy process ⋮ \(L^p\) optimal prediction of the last zero of a spectrally negative Lévy process ⋮ Optimal stopping with private information ⋮ Optimal stopping problems for running minima with positive discounting rates ⋮ Quickest detection of a hidden target and extremal surfaces ⋮ Predicting the time at which a Lévy process attains its ultimate supremum ⋮ Discounted optimal stopping problems in first-passage time models with random thresholds ⋮ Discounted Optimal Stopping Problems for Maxima of Geometric Brownian Motions With Switching Payoffs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quickest detection of a hidden target and extremal surfaces
• Predicting the ultimate supremum of a stable Lévy process with no negative jumps
• The trap of complacency in predicting the maximum
• Pathwise inequalities for local time: Applications to Skorokhod embeddings and optimal stopping
• Examples of optimal prediction in the infinite horizon case
• The Skorokhod embedding problem and its offspring
• \(\pi \) options
• On the expected diameter of an \(L_{2}\)-bounded martingale
• On the joint distribution of the maximum and its location for a linear diffusion
• Optimal stopping and best constants for Doob-like inequalities. I: The case \(p=1\)
• Optimal stopping of the maximum process: The maximality principle
• Selling a stock at the ultimate maximum
• Discounted optimal stopping for maxima in diffusion models with finite horizon
• Discounted optimal stopping problems for the maximum process
• Stopping Brownian Motion Without Anticipation as Close as Possible to Its Ultimate Maximum
• Optimal stopping of the maximum process: a converse to the results of Peskir
• Predicting the last zero of Brownian motion with drift
• Predicting the Time of the Ultimate Maximum for Brownian Motion with Drift
• On Conditional-Extremal Problems of the Quickest Detection of Nonpredictable Times of the Observable Brownian Motion
• Path Decomposition and Continuity of Local Time for One-Dimensional Diffusions, I
• Optimal prediction of the ultimate maximum of Brownian motion
• A maximal inequality for skew Brownian motion
• On a stochastic version of the trading rule “Buy and Hold”
• A Change-of-Variable Formula with Local Time on Surfaces
• The Maximality Principle Revisited: On Certain Optimal Stopping Problems
• Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes
• On a Property of the Moment at Which Brownian Motion Attains Its Maximum and Some Optimal Stopping Problems

This page was built for publication: Three-dimensional Brownian motion and the golden ratio rule