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引用次数: 0
摘要
由于在定价和套期保值中的应用，马氏最优运输在数学金融学中获得了极大的关注。马丁格尔最优运输与传统最优运输之间的一个关键区别因素是孔雀概念，孔雀是指满足凸序特性的计量序列。在传统最优运输领域，以距离的 p 次幂为成本的运输问题所引发的瓦瑟斯坦几何提供了宝贵的几何见解。这促使我们研究有马丁格尔约束和无马丁格尔约束的瓦瑟斯坦几何之间的差异。作为第一步，本文重点研究凸序的拓扑特性，目的是为进一步探索马氏瓦瑟斯坦几何的几何特性奠定基础。
Topological properties of convex order in Wasserstein metric spaces
Martingale optimal transportation has gained significant attention in mathematical finance due to its applications in pricing and hedging. A key distinguishing factor between martingale optimal transportation and traditional optimal transportation is the concept of a peacock, which refers to a sequence of measures satisfying the convex order property. In the realm of traditional optimal transportation, the Wasserstein geometry, induced by a transportation problem with the p-th power of distance as the cost, provides valuable geometric insights. This motivates us to investigate the differences between Wasserstein geometries with and without the martingale constraint. As a first step, this paper focuses on studying the topological properties of convex order, with the aim of establishing a foundational understanding for further exploration of the geometric properties of martingale Wasserstein geometry.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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