Advanced Search
MyIDEAS: Login to save this article or follow this journal

From Discrete- to Continuous-Time Finance: Weak Convergence of the Financial Gain Process


Author Info

  • Darrell Duffie
  • Philip Protter


Conditions suitable for applications in finance are given for the weak convergence (or convergence in probability) of stochastic integrals. For example, consider a sequence "S-super-n" of security price processes converging in distribution to "S" and a sequence θ-super-n of trading strategies converging in distribution to "θ". We survey conditions under which the financial gain process "θ-super-n dS-super-n" converges in distribution to "θ dS." Examples include convergence from discrete- to continuous-time settings and, in particular, generalizations of the convergence of binomial option replication models to the Black-Scholes model. Counterexamples are also provided. Copyright 1992 Blackwell Publishers.

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:
File Function: link to full text
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 2 (1992)
Issue (Month): 1 ()
Pages: 1-15

as in new window
Handle: RePEc:bla:mathfi:v:2:y:1992:i:1:p:1-15

Contact details of provider:
Web page:

Order Information:

Related research



No references listed on IDEAS
You can help add them by filling out this form.


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

Cited by:
  1. Zhao, Guoqing, 2009. "Lenglart domination inequalities for g-expectations," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2338-2342, November.
  2. Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2003. "Asymptotic Properties of Monte Carlo Estimators of Diffusion Processes," CIRANO Working Papers 2003s-11, CIRANO.
  3. Chan, K. S. & Stramer, O., 1998. "Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 33-44, August.
  4. Yan Dolinsky & Halil Soner, 2013. "Duality and convergence for binomial markets with friction," Finance and Stochastics, Springer, vol. 17(3), pages 447-475, July.
  5. Jesús P. Colino, 2008. "Weak convergence in credit risk," Statistics and Econometrics Working Papers ws085518, Universidad Carlos III, Departamento de Estadística y Econometría.
  6. Christian Bayer & Ulrich Horst & Jinniao Qiu, 2014. "A Functional Limit Theorem for Limit Order Books," Papers 1405.5230,


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


Access and download statistics


When requesting a correction, please mention this item's handle: RePEc:bla:mathfi:v:2:y:1992:i:1:p:1-15. 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: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).

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.