Structural properties of multi-period martingale optimal transport problems and applications

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2025-09-25 DOI:10.1016/j.apm.2025.116466

Brendan Pass, Joshua Hiew

{"title":"Structural properties of multi-period martingale optimal transport problems and applications","authors":"Brendan Pass, Joshua Hiew","doi":"10.1016/j.apm.2025.116466","DOIUrl":null,"url":null,"abstract":"<div><div>This paper develops new tools to study the structural properties of solutions to multi-period martingale optimal transport (MOT) problems. More precisely, conditions are obtained on how and when two-period martingale couplings may be glued together to obtain multi-period martingales and which among these gluings are optimal for particular MOT problems. Together with a novel linearization of the optimal cost as certain terms vanish, these gluing are used to obtain a complete characterization of limiting solutions in a three-period problem as the interaction between two of the variables vanishes. For the full three-period problem, several structural and uniqueness results under a variety of different assumptions on the marginals and cost function are also obtained. For high-dimensional input data, these approximation methods, if compared with classic direct numerical approximations, are cost-efficient. To illustrate the practicality of these results approximate model independent upper and lower bounds are computed for options prices depending on Amazon stock prices at three different times.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"151 ","pages":"Article 116466"},"PeriodicalIF":4.4000,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematical Modelling","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0307904X25005402","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

This paper develops new tools to study the structural properties of solutions to multi-period martingale optimal transport (MOT) problems. More precisely, conditions are obtained on how and when two-period martingale couplings may be glued together to obtain multi-period martingales and which among these gluings are optimal for particular MOT problems. Together with a novel linearization of the optimal cost as certain terms vanish, these gluing are used to obtain a complete characterization of limiting solutions in a three-period problem as the interaction between two of the variables vanishes. For the full three-period problem, several structural and uniqueness results under a variety of different assumptions on the marginals and cost function are also obtained. For high-dimensional input data, these approximation methods, if compared with classic direct numerical approximations, are cost-efficient. To illustrate the practicality of these results approximate model independent upper and lower bounds are computed for options prices depending on Amazon stock prices at three different times.

查看原文本刊更多论文

多周期鞅最优输运问题的结构性质及其应用

本文开发了研究多周期鞅最优运输问题解的结构性质的新工具。更准确地说，得到了如何以及何时将两周期鞅耦合粘合在一起以获得多周期鞅的条件，以及对于特定的MOT问题，这些粘合中哪种是最优的。结合一种新颖的最优代价线性化方法，当某些项消失时，这些粘接方法被用来获得当两个变量之间的相互作用消失时三周期问题的极限解的完整表征。对于全三周期问题，在各种不同的边际和成本函数假设下，得到了若干结构性和唯一性结果。对于高维输入数据，这些近似方法，如果与经典的直接数值近似相比，是经济有效的。为了说明这些结果的实用性，根据三个不同时间的亚马逊股票价格计算了近似模型无关的期权价格上界和下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.