Rating
1644
Battle Count: 50
Relevance
8/10
Highly relevant for quantitative finance, specifically for the calibration of local volatility models and constructing martingale couplings that respect market-implied marginals while maintaining dynamics close to a reference model (e.g., Brownian motion).
Implementation Complexity
7/10
Implementing the generalized Sinkhorn algorithm requires handling convex optimization, optimal transport solvers (for Brenier potentials), and state-dependent kernels. The one-dimensional fixed-point iteration is simpler but requires careful handling of quantile functions and integrals.
Reproducibility
3/5
The paper provides full mathematical definitions, algorithmic steps (Algorithm 1), and theoretical proofs. However, no public code repository is linked in the text, and it is a theoretical paper without empirical datasets.
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 ∈ 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.
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