Advanced Search
MyIDEAS: Login to save this paper or follow this series

Fokker-Planck and Chapman-Kolmogorov equations for Ito processes with finite memory

Contents:

Author Info

  • McCauley, Joseph L.

Abstract

The usual derivation of the Fokker-Planck partial differential eqn. (pde) assumes the Chapman-Kolmogorov equation for a Markov process [1,2]. Starting instead with an Ito stochastic differential equation (sde), we argue that finitely many states of memory are allowed in Kolmogorov’s two pdes, K1 (the backward time pde) and K2 (the Fokker-Planck pde), and show that a Chapman-Kolmogorov eqn. follows as well. We adapt Friedman’s derivation [3] to emphasize that finite memory is not excluded. We then give an example of a Gaussian transition density with 1-state memory satisfying both K1, K2, and the Chapman-Kolmogorov eqns. We begin the paper by explaining the meaning of backward time diffusion, and end by using our interpretation to produce a very short proof that the Green function for the Black-Scholes pde describes a Martingale in the risk neutral discounted stock price.

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://mpra.ub.uni-muenchen.de/2128/
File Function: original version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 2128.

as in new window
Length:
Date of creation: 22 Feb 2007
Date of revision:
Handle: RePEc:pra:mprapa:2128

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC

Related research

Keywords: Stochastic process; martingale; Ito process; stochastic differential eqn.; memory; nonMarkov process; 2 backward time diffusion; Fokker-Planck; Kolmogorov’s partial differential eqns.; Chapman-Kolmogorov eqn.; Black- Scholes eqn;

Find related papers by JEL classification:

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. McCauley, Joseph L. & Gunaratne, Gemunu H. & Bassler, Kevin E., 2007. "Martingale option pricing," MPRA Paper 2151, University Library of Munich, Germany.
  2. Duffie, Darrell, 1988. "An extension of the Black-Scholes model of security valuation," Journal of Economic Theory, Elsevier, vol. 46(1), pages 194-204, October.
  3. J. L. McCauley & G. H. Gunaratne & K. E. Bassler, 2006. "Martingale Option Pricing," Papers physics/0606011, arXiv.org, revised Feb 2007.
  4. McCauley, J.L. & Gunaratne, G.H. & Bassler, K.E., 2007. "Martingale option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 351-356.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu H., 2007. "Martingales, Detrending Data, and the Efficient Market Hypothesis," MPRA Paper 2256, University Library of Munich, Germany.
  2. McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu h., 2007. "Martingales, the efficient market hypothesis, and spurious stylized facts," MPRA Paper 5303, University Library of Munich, Germany.

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:pra:mprapa:2128. 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: (Ekkehart Schlicht).

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.