IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v2y1992i1p1-15.html
   My bibliography  Save this article

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

Author

Listed:
  • Darrell Duffie
  • Philip Protter

Abstract

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.

Suggested Citation

  • Darrell Duffie & Philip Protter, 1992. "From Discrete- to Continuous-Time Finance: Weak Convergence of the Financial Gain Process," Mathematical Finance, Wiley Blackwell, vol. 2(1), pages 1-15.
  • Handle: RePEc:bla:mathfi:v:2:y:1992:i:1:p:1-15
    as

    Download full text from publisher

    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9965.1992.tb00022.x
    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 search for a different version of it.

    Citations

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


    Cited by:

    1. Yan Dolinsky & Halil Soner, 2013. "Duality and convergence for binomial markets with friction," Finance and Stochastics, Springer, vol. 17(3), pages 447-475, July.
    2. repec:dau:papers:123456789/5374 is not listed on IDEAS
    3. Liang, Hanying & Phillips, Peter C.B. & Wang, Hanchao & Wang, Qiying, 2016. "Weak Convergence To Stochastic Integrals For Econometric Applications," Econometric Theory, Cambridge University Press, vol. 32(06), pages 1349-1375, December.
    4. Kraft, Holger & Seifried, Frank Thomas, 2014. "Stochastic differential utility as the continuous-time limit of recursive utility," Journal of Economic Theory, Elsevier, vol. 151(C), pages 528-550.
    5. 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.
    6. Qiao, Gaoxiu & Yao, Qiang, 2015. "Weak convergence of equity derivatives pricing with default risk," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 46-56.
    7. Colino, Jesús P., 2008. "Weak convergence in credit risk," DES - Working Papers. Statistics and Econometrics. WS ws085518, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
    9. Detemple, Jerome & Garcia, Rene & Rindisbacher, Marcel, 2006. "Asymptotic properties of Monte Carlo estimators of diffusion processes," Journal of Econometrics, Elsevier, vol. 134(1), pages 1-68, September.
    10. Zhao, Guoqing, 2009. "Lenglart domination inequalities for g-expectations," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2338-2342, November.
    11. Kasper Larsen, 2009. "Continuity Of Utility-Maximization With Respect To Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 237-250.
    12. Peter Bank & Yan Dolinsky & Ari-Pekka Perkkiö, 2017. "The scaling limit of superreplication prices with small transaction costs in the multivariate case," Finance and Stochastics, Springer, vol. 21(2), pages 487-508, April.
    13. Christian Bayer & Ulrich Horst & Jinniao Qiu, 2014. "A Functional Limit Theorem for Limit Order Books with State Dependent Price Dynamics," Papers 1405.5230, arXiv.org, revised Aug 2016.
    14. Dolinsky, Yan & Nutz, Marcel & Soner, H. Mete, 2012. "Weak approximation of G-expectations," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 664-675.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.

    We have no references for this item. You can help adding them by using 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.