IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v14y2026i6p968-d1891936.html

Agent-Based Models for Two Stocks with Superhedging

Author

Listed:
  • Dario Crisci

    (Department of Mathematics, Toronto Metropolitan University, 350 Victoria Treet, Toronto, ON M5B 2K3, Canada)

  • Sebastian Ferrando

    (Department of Mathematics, Toronto Metropolitan University, 350 Victoria Treet, Toronto, ON M5B 2K3, Canada)

  • Konrad Gajewski

    (Department of Mathematics, Toronto Metropolitan University, 350 Victoria Treet, Toronto, ON M5B 2K3, Canada)

Abstract

We propose an agent-based, non-probabilistic framework for modeling the joint evolution of two discounted asset prices expressed in units of a third asset acting as numeraire. The framework is based on a trajectorial superhedging theory, in which pricing, arbitrage, and null events are defined purely in financial terms, without reference to probability measures or martingale assumptions. A central necessary theoretical requirement is that the global property ( L ) -a.e. holds, ensuring consistency of the model construction. Admissible price evolutions are described by multidimensional trajectory sets generated from observable price movements and operational rebalancing rules representing a prescribed class of agents. Within a fixed trajectory set, relative price bounds between the two assets are obtained via superhedging and subhedging by means of self-financing portfolios that trade one asset against the other.

Suggested Citation

  • Dario Crisci & Sebastian Ferrando & Konrad Gajewski, 2026. "Agent-Based Models for Two Stocks with Superhedging," Mathematics, MDPI, vol. 14(6), pages 1-53, March.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:6:p:968-:d:1891936
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/14/6/968/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/14/6/968/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;

    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:gam:jmathe:v:14:y:2026:i:6:p:968-:d:1891936. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (email available below). General contact details of provider: https://www.mdpi.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.