英文标题：
《Sampling of probability measures in the convex order by Wasserstein
projection》
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作者：
Aur\\\'elien Alfonsi, Jacopo Corbetta and Benjamin Jourdain
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最新提交年份：
2019
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英文摘要：
In this paper, for $\\mu$ and $\\nu$ two probability measures on $\\mathbb{R}^d$ with finite moments of order $\\rho\\ge 1$, we define the respective projections for the $W_\\rho$-Wasserstein distance of $\\mu$ and $\\nu$ on the sets of probability measures dominated by $\\nu$ and of probability measures larger than $\\mu$ in the convex order. The $W_2$-projection of $\\mu$ can be easily computed when $\\mu$ and $\\nu$ have finite support by solving a quadratic optimization problem with linear constraints. In dimension $d=1$, Gozlan et al.~(2018) have shown that the projections do not depend on $\\rho$. We explicit their quantile functions in terms of those of $\\mu$ and $\\nu$. The motivation is the design of sampling techniques preserving the convex order in order to approximate Martingale Optimal Transport problems by using linear programming solvers. We prove convergence of the Wasserstein projection based sampling methods as the sample sizes tend to infinity and illustrate them by numerical experiments.
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中文摘要：
本文中，对于$\\mu$和$\\nu$两个在$\\mathbb{R}^d$上具有$\\rho\\ge 1$阶有限矩的概率测度，我们定义了$\\mu$和$\\nu$的$\\W\\rho$-Wasserstein距离在$\\nu$支配的概率测度集和凸阶大于$\\mu$的概率测度集上的相应投影。当$\\ mu$和$\\ nu$具有有限的支持度时，通过求解具有线性约束的二次优化问题，可以很容易地计算$\\ mu$的$\\ W\\u 2$-投影。在维度$d=1$中，Gozlan et al.（2018）表明预测不依赖于$\\ rho$。我们用$\\ mu$和$\\ nu$的分位数函数来表示它们的分位数函数。其动机是设计保持凸序的采样技术，以便使用线性规划求解器逼近鞅最优运输问题。当样本量趋于无穷大时，我们证明了基于Wasserstein投影的采样方法的收敛性，并通过数值实验加以说明。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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