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qx-Bass Martingales: Optimality, Existence and Convergence

  • Antonio Marini
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Abstract

We introduce the class of qx-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 (qx)x ∈ ℝd in the sense of a suitable weak optimal transport problem. We show that qx-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.

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Cite

BibTeXRIS
BibTeX
@misc{marini2026qxbass,
  title = {{$q_x$-Bass Martingales: Optimality, Existence and Convergence}},
  author = {Antonio Marini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20920},
  eprint = {2610.20920},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20920},
}
RIS
TY  - UNPB
TI  - q_x-Bass Martingales: Optimality, Existence and Convergence
AU  - Antonio Marini
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20920
UR  - https://arxiv.org/abs/2610.20920
AB  - 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 ∈ 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.
ER  -