Reflected Mean-Field Backward Stochastic Differential Equations. Approximation and Associated Nonlinear PDEs
Reflected Mean-Field Backward Stochastic Differential Equations. Approximation and Associated Nonlinear PDEs
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反射平均场后向随机微分方程。
DOI：
10.1016/j.jmaa.2013.11.028
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发表时间：
2012-10
影响因子：
1.3
通讯作者：
Juan Li
中科院分区：
文献类型：
--
作者：
Juan Li
数学平均场方法在许多领域都有应用，不仅在物理和化学领域，而且最近在金融、经济学和博弈论领域也有应用。本文用纯概率方法研究了一类新的特殊平均场问题，并刻画了它的极限，即带反射的平均场倒向随机微分方程的解。另一方面，我们将用惩罚法证明这类反射平均场BSDEs也可以作为平均场BSDEs的极限方程得到。最后，利用反射平均场偏微分方程的解，给出了带有障碍物的非线性非局部偏微分方程的概率解释。
Mathematical mean-field approaches have been used in many fields, not only in Physics and Chemistry, but also recently in Finance, Economics, and Game Theory. In this paper we will study a new special mean-field problem in a purely probabilistic method, to characterize its limit which is the solution of mean-field backward stochastic differential equations (BSDEs) with reflections. On the other hand, we will prove that this type of reflected mean-field BSDEs can also be obtained as the limit equation of the mean-field BSDEs by penalization method. Finally, we give the probabilistic interpretation of the nonlinear and nonlocal partial differential equations with the obstacles by the solutions of reflected mean-field BSDEs.
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影响因子：
--
作者：
Y. Achdou;P. Cardaliaguet;François Delarue;A. Porretta;Filippo Santambrogio
通讯作者：
Y. Achdou;P. Cardaliaguet;François Delarue;A. Porretta;Filippo Santambrogio
影响因子：
1.8
作者：
Daniel Andersson;Boualem Djehiche
通讯作者：
Daniel Andersson;Boualem Djehiche
影响因子：
1.6
作者：
P. Pra;F. Hollander
通讯作者：
P. Pra;F. Hollander
影响因子：
1.6
作者：
El Karoui, N;Peng, S;Quenez, MC
通讯作者：
Quenez, MC
影响因子：
2.3
作者：
R. Buckdahn;Boualem Djehiche;Juan Li;S. Peng
通讯作者：
R. Buckdahn;Boualem Djehiche;Juan Li;S. Peng