RBDSDEs with jumps and optional Barrier and mean field game with common noise

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE

Finance and Stochastics Pub Date : 2022-08-30 DOI:10.1080/17442508.2022.2113080

Badr-eddine Berrhazi, M. El Fatini, A. Hilbert, N. Mrhardy, R. Pettersson

引用次数: 0

Abstract

ABSTRACT In this paper, we study a generalization of reflected backward doubly stochastic differential equations (RBDSDEs) and present a link to a general mean field game. In our case, the RBDSDEs are associated with a lower optional not right continuous barrier. First, we establish the existence and uniqueness of a solution of such RBDSDEs. We then study a mean field game with a new type of common noise related to an electricity grid with storage allowing jumps and prove the existence of a mean field Nash equilibrium.

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RBDSDEs与跳跃和可选的障碍和平均场游戏与常见的噪音

摘要本文研究了反射后向双随机微分方程(RBDSDEs)的推广，并给出了与一般平均场对策的联系。在我们的例子中，rbdsde与较低的可选非右连续屏障相关联。首先，我们建立了这类RBDSDEs解的存在唯一性。然后，我们研究了一种与允许跳跃的存储电网相关的新型公共噪声的平均场博弈，并证明了平均场纳什均衡的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finance and Stochastics 管理科学-数学跨学科应用

CiteScore

2.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Finance and Stochastics is to provide a high standard publication forum for research - in all areas of finance based on stochastic methods - on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance. Finance and Stochastics encompasses - but is not limited to - the following fields: - theory and analysis of financial markets - continuous time finance - derivatives research - insurance in relation to finance - portfolio selection - credit and market risks - term structure models - statistical and empirical financial studies based on advanced stochastic methods - numerical and stochastic solution techniques for problems in finance - intertemporal economics, uncertainty and information in relation to finance.