Shadow martingales – a stochastic mass transport approach to the peacock problem

@article{Bruckerhoff2020ShadowM,
  title={Shadow martingales – a stochastic mass transport approach to the peacock problem},
  author={Martin Bruckerhoff and Martin Huesmann and Nicolas Juillet},
  journal={Electronic Journal of Probability},
  year={2020}
}
Given a family of real probability measures $(\mu_t)_{t\geq 0}$ increasing in convex order (a peacock) we describe a systematic method to create a martingale exactly fitting the marginals at any time. The key object for our approach is the obstructed shadow of a measure in a peacock, a generalization of the (obstructed) shadow introduced in \cite{BeJu16,NuStTa17}. As input data we take an increasing family of measures $(\nu^\alpha)_{\alpha \in [0,1]}$ with $\nu^\alpha(\mathbb{R})=\alpha$ that… 

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