Advanced Search
MyIDEAS: Login

Three-Dimensional Brownian Motion and the Golden Ratio Rule

Contents:

Author Info

Abstract

Let X =(Xt)t=0 be a transient diffusion processin (0,8) with the diffusion coeffcient s> 0 and the scale function L such that Xt ?8 as t ?8 ,let It denote its running minimum for t = 0, and let ? denote the time of its ultimate minimum I8 .Setting c(i,x)=1-2L(x)/L(i) we show that the stopping time minimises E(|? - t|- ?) over all stopping times t of X (with finite mean) where the optimal boundary f* can be characterised as the minimal solution to staying strictly above the curve h(i)= L-1(L(i)/2) for i > 0. In particular, when X is the radial part of three-dimensional Brownian motion, we find that where ? =(1+v5)/2=1.61 ... is the golden ratio. The derived results are applied to problems of optimal trading in the presence of bubbles where we show that the golden ratio rule offers a rigourous optimality argument for the choice of the well known golden retracement in technical analysis of asset prices.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp295.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 295.

as in new window
Length: 27
Date of creation: 01 Aug 2011
Date of revision:
Handle: RePEc:uts:rpaper:295

Contact details of provider:
Postal: PO Box 123, Broadway, NSW 2007, Australia
Phone: +61 2 9514 7777
Fax: +61 2 9514 7711
Web page: http://www.qfrc.uts.edu.au/
More information through EDIRC

Related research

Keywords:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(04), pages 533-554, November.
  2. A. M. G. Cox & David Hobson & Jan Ob{\l}\'oj, 2007. "Pathwise inequalities for local time: Applications to Skorokhod embeddings and optimal stopping," Papers math/0702173, arXiv.org, revised Nov 2008.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:295. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.