论文标题
如何在保留凸订单的同时量化概率
How to quantise probabilities while preserving their convex order
论文作者
论文摘要
我们介绍了一种算法，该算法，给定概率$μ\ leq _ {\ text {cx}}ν$按顺序定义，并在可分开的banach space $ b $上定义，构建有限支持的近似值$μ_n\ toμ，ν_n\ to n in convex $ convex $ convex $μ \ leq _ {\ text {cx}}ν_n$。我们以瓦斯汀距离为收敛速度提供上限。我们讨论了算法的优势及其与Martingale最佳运输问题的离散化的联系，并通过数值示例说明了其实施。我们研究了$ $ $/$ν$和一些（有限）$ b $的操作，输出$μ_n$/$ $/$ n $，表明适用于概率$γ$，并将其输出所有概率的所有分区，以输出所有概率$ $ q \ leq _ {\ leq _ {\ fext {\ cx {cx {cx}}γ$。
We introduce an algorithm which, given probabilities $μ\leq_{\text{cx}} ν$ in convex order and defined on a separable Banach space $B$, constructs finitely-supported approximations $μ_n \to μ, ν_n\to ν$ which are in convex order $μ_n \leq_{\text{cx}} ν_n$. We provide upper-bounds for the speed of convergence, in terms of the Wasserstein distance. We discuss the (dis)advantages of our algorithm and its link with the discretisation of the Martingale Optimal Transport problem, and we illustrate its implementation with numerical examples. We study the operation which, given $μ$/$ν$ and some (finite) partition of $B$, outputs $μ_n$/$ν_n$, showing that applied to a probability $γ$ and to all partitions it outputs the set of all probabilities $ζ\leq_{\text{cx}} γ$.
