Martingale Schrödinger bridges extend to any dimension, minimize weighted quadratic energy from Brownian motion in continuous time, and coincide with Föllmer martingales in irreducible cases.
arXiv preprint arXiv:1904.04554 , year=
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abstract
Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas, options on realized variance or VIX options. These models differ strongly from the well-known local stochastic volatility models, in particular the instantaneous volatility-of-volatility of the associated naked SVMs is not modified, once calibrated to market instruments. They can be interpreted as a martingale version of the Schrodinger bridge. The numerical calibration is performed using a dynamic-like version of the Sinkhorn algorithm. We finally highlight a striking relation with Dyson non-colliding Brownian motions.
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2026 2verdicts
UNVERDICTED 2representative citing papers
A generative transfer framework using iterative path-wise tilting integrated with conditional flow matching recovers target entropic optimal transport couplings from reference samples, achieving O(δ) convergence in Wasserstein-1 distance.
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Bridging classical and martingale Schr\"odinger bridges
Martingale Schrödinger bridges extend to any dimension, minimize weighted quadratic energy from Brownian motion in continuous time, and coincide with Föllmer martingales in irreducible cases.
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Generative Transfer for Entropic Optimal Transport with Unknown Costs
A generative transfer framework using iterative path-wise tilting integrated with conditional flow matching recovers target entropic optimal transport couplings from reference samples, achieving O(δ) convergence in Wasserstein-1 distance.