[图书][B] Probabilistic theory of mean field games with applications I-II

R Carmona, F Delarue - 2018 - Springer
The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …

[图书][B] A probabilistic approach to classical solutions of the master equation for large population equilibria

JF Chassagneux, D Crisan, F Delarue - 2022 - ams.org
We analyze a class of nonlinear partial differential equations (PDEs) defined on $\mathbb
{R}^ d\times\mathcal {P} _2 (\mathbb {R}^ d), $ where $\mathcal {P} _2 (\mathbb {R}^ d) $ is …

[图书][B] Contract theory in continuous-time models

J Cvitanic, J Zhang - 2012 - books.google.com
In recent years there has been a significant increase of interest in continuous-time Principal-
Agent models, or contract theory, and their applications. Continuous-time models provide a …

[图书][B] Backward stochastic differential equations

J Zhang, J Zhang - 2017 - Springer
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[图书][B] Backward stochastic differential equations with jumps and their actuarial and financial applications

Ł Delong - 2013 - Springer
A linear backward stochastic differential equation was introduced by Bismut (1973) in an
attempt to solve an optimal stochastic control problem by the maximum principle. The …

A probabilistic approach to mean field games with major and minor players

R Carmona, X Zhu - 2016 - projecteuclid.org
We propose a new approach to mean field games with major and minor players. Our
formulation involves a two player game where the optimization of the representative minor …

Selection of equilibria in a linear quadratic mean-field game

F Delarue, RF Tchuendom - Stochastic Processes and their Applications, 2020 - Elsevier
In this paper, we address an instance of uniquely solvable mean-field game with a common
noise whose corresponding counterpart without common noise has several equilibria. We …

Wellposedness of second order master equations for mean field games with nonsmooth data

C Mou, J Zhang - arXiv preprint arXiv:1903.09907, 2019 - arxiv.org
In this paper we study second order master equations arising from mean field games with
common noise over arbitrary time duration. A classical solution typically requires the …

Mean field type control problems, some Hilbert-space-valued FBSDEs, and related equations

A Bensoussan, HM Tai, SCP Yam - arXiv preprint arXiv:2305.04019, 2023 - arxiv.org
In this article, we provide an original systematic global-in-time analysis of mean field type
control problems on $\mathbb {R}^ n $ with generic cost functionals by the modified …

A global stochastic maximum principle for fully coupled forward-backward stochastic systems

M Hu, S Ji, X Xue - SIAM Journal on Control and Optimization, 2018 - SIAM
We study a stochastic optimal control problem for fully coupled forward-backward stochastic
control systems with a nonempty control domain. For our problem, the first-order and second …