$L^{p}$ SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS

doi:10.1007/s10473-020-0417-x

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (4): 1116-1140.doi: 10.1007/s10473-020-0417-x

$L^{p}$ SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS

陈雅洁¹, 邢传智², 张晓²

1. Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China;
2. School of Mathematics and Statistics, Shandong University, Weihai 264209, China

收稿日期:2019-03-12 修回日期:2019-12-24 出版日期:2020-08-25 发布日期:2020-08-21
通讯作者: Chuanzhi XING E-mail:chuanzhixing@mail.sdu.edu.cn
作者简介:Yajie CHEN,E-mail:yajiechen@mail.sdu.edu.cn;Xiao ZHANG,E-mail:zhangxiao176@126.com
基金资助:
The work was supported in part by the NSFC (11222110; 11871037), Shandong Province (JQ201202), NSFC-RS (11661130148; NA150344), 111 Project (B12023).

$L^{p}$ SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS

Yajie CHEN¹, Chuanzhi XING², Xiao ZHANG²

1. Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China;
2. School of Mathematics and Statistics, Shandong University, Weihai 264209, China

Received:2019-03-12 Revised:2019-12-24 Online:2020-08-25 Published:2020-08-21
Contact: Chuanzhi XING E-mail:chuanzhixing@mail.sdu.edu.cn
Supported by:
The work was supported in part by the NSFC (11222110; 11871037), Shandong Province (JQ201202), NSFC-RS (11661130148; NA150344), 111 Project (B12023).

摘要/Abstract

摘要： In this paper we consider one dimensional mean-field backward stochastic differential equations (BSDEs) under weak assumptions on the coefficient. Unlike [3], the generator of our mean-field BSDEs depends not only on the solution $(Y,Z)$ but also on the law $P_{Y}$ of $Y$. The first part of the paper is devoted to the existence and uniqueness of solutions in $L^p$, $1< p\leq2$, where the monotonicity conditions are satisfied. Next, we show that if the generator $f$ is uniformly continuous in $(\mu,y,z)$, uniformly with respect to $(t,\omega)$, and if the terminal value $\xi$ belongs to $L^{p}(\Omega,\mathcal{F},P)$ with $1

关键词: general mean-field backward stochastic differential equations, monotonicity condition, continuous condition, uniformly continuous condition, L^{p

Abstract: In this paper we consider one dimensional mean-field backward stochastic differential equations (BSDEs) under weak assumptions on the coefficient. Unlike [3], the generator of our mean-field BSDEs depends not only on the solution $(Y,Z)$ but also on the law $P_{Y}$ of $Y$. The first part of the paper is devoted to the existence and uniqueness of solutions in $L^p$, $1< p\leq2$, where the monotonicity conditions are satisfied. Next, we show that if the generator $f$ is uniformly continuous in $(\mu,y,z)$, uniformly with respect to $(t,\omega)$, and if the terminal value $\xi$ belongs to $L^{p}(\Omega,\mathcal{F},P)$ with $1

Key words: general mean-field backward stochastic differential equations, monotonicity condition, continuous condition, uniformly continuous condition, L^{p

中图分类号:

60H10

陈雅洁, 邢传智, 张晓. $L^{p}$ SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS[J]. 数学物理学报(英文版), 2020, 40(4): 1116-1140.

Yajie CHEN, Chuanzhi XING, Xiao ZHANG. $L^{p}$ SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS[J]. Acta mathematica scientia,Series B, 2020, 40(4): 1116-1140.

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$L^{p}$ SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS

$L^{p}$ SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS

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