一维价格形成模型的变分法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-07 DOI:10.4310/cms.2024.v22.n1.a10

Yuri Ashrafyan, Tigran Bakaryan, Diogo Gomes, Julian Gutierrez

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引用次数: 2

摘要

本文研究了一类以价格形成为模型的一阶均值场博弈（MFGs）。我们利用波恩卡莱（Poincaré）两难法消除了 MFGs 系统中的一个方程，得到了一个单一函数的变分问题。我们证明了变分问题解的唯一性，并通过应用松弛论证解决了解的存在性问题。此外，我们还建立了 MFGs 系统的解与变分问题之间的对应关系。基于这种对应关系，我们为原始 MFGs 问题的求解引入了另一种数值方法。最后，我们以线性二次模型的数值结果结束本文。

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A variational approach for price formation models in one dimension

In this paper, we study a class of first-order mean-field games (MFGs) that model price formation. Using Poincaré lemma, we eliminate one of the equations of the MFGs system and obtain a variational problem for a single function. We prove the uniqueness of the solutions to the variational problem and address the existence of solutions by applying relaxation arguments. Moreover, we establish a correspondence between solutions of the MFGs system and the variational problem. Based on this correspondence, we introduce an alternative numerical approach for the solution of the original MFGs problem. We end the paper with numerical results for a linear-quadratic model.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.