Well-posedness of mean-field type forward-backward stochastic differential equations

A. Bensoussan; S. C P Yam; Z. Zhang

doi:10.1016/j.spa.2015.04.006

Well-posedness of mean-field type forward-backward stochastic differential equations

A. Bensoussan, S. C P Yam^*, Z. Zhang

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

60 Citations (Scopus)

Abstract

Abstract Being motivated by a recent pioneer work Carmona and Delarue (2013), in this article, we propose a broad class of natural monotonicity conditions under which the unique existence of the solutions to Mean-Field Type (MFT) Forward-Backward Stochastic Differential Equations (FBSDE) can be established. Our conditions provided here are consistent with those normally adopted in the traditional FBSDE (without the interference of a mean-field) frameworks, and give a generic explanation on the unique existence of solutions to common MFT-FBSDEs, such as those in the linear-quadratic setting; besides, the conditions are 'optimal' in a certain sense that can elaborate on how their counter-example in Carmona and Delarue (2013) just fails to ensure its well-posedness. Finally, a stability theorem is also included.

Original language	English
Article number	2778
Pages (from-to)	3327-3354
Journal	Stochastic Processes and their Applications
Volume	125
Issue number	9
DOIs	https://doi.org/10.1016/j.spa.2015.04.006
Publication status	Published - 1 Sept 2015

Research Keywords

Forward-backward stochastic differential equations
Linear-quadratic setting
Mean-field type
Monotonicity conditions
Well-posedness

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title = "Well-posedness of mean-field type forward-backward stochastic differential equations",

abstract = "Abstract Being motivated by a recent pioneer work Carmona and Delarue (2013), in this article, we propose a broad class of natural monotonicity conditions under which the unique existence of the solutions to Mean-Field Type (MFT) Forward-Backward Stochastic Differential Equations (FBSDE) can be established. Our conditions provided here are consistent with those normally adopted in the traditional FBSDE (without the interference of a mean-field) frameworks, and give a generic explanation on the unique existence of solutions to common MFT-FBSDEs, such as those in the linear-quadratic setting; besides, the conditions are 'optimal' in a certain sense that can elaborate on how their counter-example in Carmona and Delarue (2013) just fails to ensure its well-posedness. Finally, a stability theorem is also included.",

keywords = "Forward-backward stochastic differential equations, Linear-quadratic setting, Mean-field type, Monotonicity conditions, Well-posedness",

author = "A. Bensoussan and Yam, {S. C P} and Z. Zhang",

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T1 - Well-posedness of mean-field type forward-backward stochastic differential equations

AU - Bensoussan, A.

AU - Yam, S. C P

AU - Zhang, Z.

PY - 2015/9/1

Y1 - 2015/9/1

N2 - Abstract Being motivated by a recent pioneer work Carmona and Delarue (2013), in this article, we propose a broad class of natural monotonicity conditions under which the unique existence of the solutions to Mean-Field Type (MFT) Forward-Backward Stochastic Differential Equations (FBSDE) can be established. Our conditions provided here are consistent with those normally adopted in the traditional FBSDE (without the interference of a mean-field) frameworks, and give a generic explanation on the unique existence of solutions to common MFT-FBSDEs, such as those in the linear-quadratic setting; besides, the conditions are 'optimal' in a certain sense that can elaborate on how their counter-example in Carmona and Delarue (2013) just fails to ensure its well-posedness. Finally, a stability theorem is also included.

AB - Abstract Being motivated by a recent pioneer work Carmona and Delarue (2013), in this article, we propose a broad class of natural monotonicity conditions under which the unique existence of the solutions to Mean-Field Type (MFT) Forward-Backward Stochastic Differential Equations (FBSDE) can be established. Our conditions provided here are consistent with those normally adopted in the traditional FBSDE (without the interference of a mean-field) frameworks, and give a generic explanation on the unique existence of solutions to common MFT-FBSDEs, such as those in the linear-quadratic setting; besides, the conditions are 'optimal' in a certain sense that can elaborate on how their counter-example in Carmona and Delarue (2013) just fails to ensure its well-posedness. Finally, a stability theorem is also included.

KW - Forward-backward stochastic differential equations

KW - Linear-quadratic setting

KW - Mean-field type

KW - Monotonicity conditions

KW - Well-posedness

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DO - 10.1016/j.spa.2015.04.006

M3 - RGC 21 - Publication in refereed journal

SN - 0304-4149

VL - 125

SP - 3327

EP - 3354

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 9

M1 - 2778

ER -

Well-posedness of mean-field type forward-backward stochastic differential equations

Abstract

Research Keywords

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