IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2610.20920.html

$q_x$-Bass Martingales: Optimality, Existence and Convergence

Author

Listed:
  • Antonio Marini

Abstract

We introduce the class of $q_x$-Bass martingales, extending the notion of $q$-Bass martingales. These are martingale couplings with prescribed marginals whose transition kernels are closest to a given family of reference kernels $(q_x)_{x \in \mathbb R^d}$ in the sense of a suitable weak optimal transport problem. We show that $q_x$-Bass martingales are optimizers of this problem and establish a strong duality result. Building on this duality, we introduce an algorithm for their computation and, under compactness assumptions on the prescribed marginals, prove its convergence, thereby establishing existence. We then specialize to one-dimensional marginals and show that the algorithm reduces to a fixed-point iteration.

Suggested Citation

  • Antonio Marini, 2026. "$q_x$-Bass Martingales: Optimality, Existence and Convergence," Papers 2610.20920, arXiv.org.
    • Handle: RePEc:arx:papers:2610.20920
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2610.20920
    File Function: Latest version
    Download Restriction: no
    ---><---

    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:arx:papers:2610.20920. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.