Publications (34)
Mean-field backward stochastic differential equations: A limit approach
Rainer Buckdahn, Boualem Djehiche, Juan Li +1
Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application in Economics, Finance…
Brownian Bridges on Random Intervals
Matteo Ludovico Bedini, Rainer Buckdahn, Hans-Jürgen Engelbert
The issue of giving an explicit description of the flow of information concerning the time of bankruptcy of a company (or a state) arriving on the market is tackled by defining a b…
Unexpected Default in an Information Based Model
Matteo Ludovico Bedini, Rainer Buckdahn, Hans-Jürgen Engelbert
This paper provides sufficient conditions for the time of bankruptcy (of a company or a state) for being a totally inaccessible stopping time and provides the explicit computation…
A General Conditional McKean-Vlasov Stochastic Differential Equation
Rainer Buckdahn, Juan Li, Jin Ma
In this paper we consider a class of {\it conditional McKean-Vlasov SDEs} (CMVSDE for short). Such an SDE can be considered as an extended version of McKean-Vlasov SDEs with common…
Mean-field stochastic differential equations and associated PDEs
Rainer Buckdahn, Juan Li, Shige Peng +1
In this paper we consider a mean-field stochastic differential equation, also called Mc Kean-Vlasov equation, with initial data which coefficients depend…
Nonlinear stochastic differential games involving a major player and a large number of collectively acting minor agents
Rainer Buckdahn, Juan Li, Shige Peng
The purpose of this paper is to study 2-person zero-sum stochastic differential games, in which one player is a major one and the other player is a group of minor agents which…
Stochastic control problems for systems driven by normal martingales
Rainer Buckdahn, Jin Ma, Catherine Rainer
In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems…
A Mean-field Stochastic Control Problem with Partial Observations
Rainer Buckdahn, Juan Li, Jin Ma
In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficie…
Stochastic Differential Games and Viscosity Solutions of Hamilton-Jacobi-Bellman-Isaacs Equations
Rainer Buckdahn, Juan Li
In this paper we study zero-sum two-player stochastic differential games with the help of theory of Backward Stochastic Differential Equations (BSDEs). At the one hand we generaliz…
Mean field stochastic control under sublinear expectation
Rainer Buckdahn, Bowen He, Juan Li
Our work is devoted to the study of Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's -expectation. The dynamics of the controlled…
Probabilistic Interpretation for Systems of Isaacs Equations with Two Reflecting Barriers
Rainer Buckdahn, Juan Li
In this paper we investigate zero-sum two-player stochastic differential games whose cost functionals are given by doubly controlled reflected backward stochastic differential equa…
Peng's Maximum Principle for a Stochastic Control Problem Driven by a Fractional and a Standard Brownian Motion
Rainer Buckdahn, Shuai Jing
We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2. We apply an anticipative Girsanov transformation…
Mean-field BDSDEs and associated nonlocal semi-linear backward stochastic partial differential equations
Rainer Buckdahn, Juan Li, Chuanzhi Xing
In this paper we investigate mean-field backward doubly stochastic differential equations (BDSDEs), i.e., BDSDEs whose driving coefficients also depend on the joint law of the solu…
Stochastic Differential Games with Reflection and Related Obstacle Problems for Isaacs Equations
Rainer Buckdahn, Juan Li
In this paper we first investigate zero-sum two-player stochastic differential games with reflection with the help of theory of Reflected Backward Stochastic Differential Equations…
Generalized Hamilton-Jacobi-Bellman equations with Dirichlet boundary and stochastic exit time optimal control problem
Rainer Buckdahn, Tianyang Nie
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study t…
Derivative over Wasserstein spaces along curves of densities
Rainer Buckdahn, Juan Li, Hao Liang
In this paper, given any random variable defined over a probability space , we focus on the study of the derivative of functions of the form $L\mapsto F_Q(…
Inf-convolution of G-expectations
Xuepeng Bai, Rainer Buckdahn
In this paper we will discuss the optimal risk transfer problems when risk measures are generated by G-expectations, and we present the relationship between inf-convolution of G-ex…
Pathwise Taylor Expansions for Random Fields on Multiple Dimensional Paths
Rainer Buckdahn, Jin Ma, Jianfeng Zhang
In this paper we establish the pathwise Taylor expansions for random fields that are "regular" in the spirit of Dupire's path-derivatives \cite{Dupire}. Our result is motivated by…
Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions
Rainer Buckdahn, Christian Keller, Jin Ma +1
We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treate…
Path-depending controlled mean-field coupled forward-backward SDEs. The associated stochastic maximum principle
Rainer Buckdahn, Juan Li, Junsong Li +1
In the present paper we discuss a new type of mean-field coupled forward-backward stochastic differential equations (MFFBSDEs). The novelty consists in the fact that the coefficien…
Stochastic Variational Inequalities on Non-Convex Domains
Rainer Buckdahn, Lucian Maticiuc, Etienne Pardoux +1
The objective of this work is to prove, in a first step, the existence and the uniqueness of a solution of the following multivalued deterministic differential equation: $dx(t)+\pa…
Pathwise Taylor Expansions for Itô Random Fields
Rainer Buckdahn, Ingo Bulla, Jin Ma
In this paper we study the {\it pathwise stochastic Taylor expansion}, in the sense of our previous work \cite{Buckdahn_Ma_02}, for a class of Itô-type random fields in which the…
Optimal control problems with generalized mean-field dynamics and viscosity solution to Master Bellman equation
Rainer Buckdahn, Juan Li, Zhanxin Li
We study an optimal control problem of generalized mean-field dynamics with open-loop controls, where the coefficients depend not only on the state processes and controls, but also…
Another proof for the equivalence between invariance of closed sets with respect to stochastic and deterministic systems
Rainer Buckdahn, Marc Quincampoix, Catherine Rainer +1
We provide a short and elementary proof for the recently proved result by G. da Prato and H. Frankowska that -- under minimal assumptions -- a closed set is invariant with respect…
Integral-Partial Differential Equations of Isaacs' Type Related to Stochastic Differential Games with Jumps
Rainer Buckdahn, Ying Hu, Juan Li
In this paper we study zero-sum two-player stochastic differential games with jumps with the help of theory of Backward Stochastic Differential Equations (BSDEs). We generalize the…
Value Function of Differential Games without Isaacs Conditions. An Approach with Non-Anticipative Mixed Strategies
Rainer Buckdahn, Juan Li, Marc Quincampoix
In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable concept of mixed strat…
Value in mixed strategies for zero-sum stochastic differential games without Isaacs condition
Rainer Buckdahn, Juan Li, Marc Quincampoix
In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equ…
A Global Stochastic Maximum Principle for Mean-Field Forward-Backward Stochastic Control Systems with Quadratic Generators
Rainer Buckdahn, Juan Li, Yanwei Li +1
Our paper is devoted to the study of Peng's stochastic maximum principle (SMP) for a stochastic control problem composed of a controlled forward stochastic differential equation (S…
Differential games with asymmetric information and without Isaacs condition
Rainer Buckdahn, Marc Quincampoix, Catherine Rainer +1
We investigate a two-player zero-sum differential game with asymmetric information on the payoff and without Isaacs condition. The dynamics is an ordinary differential equation par…
Regularity properties for general HJB equations. A BSDE method
Rainer Buckdahn, Jianhui Huang, Juan Li
In this work we investigate regularity properties of a large class of Hamilton-Jacobi-Bellman (HJB) equations with or without obstacles, which can be stochastically interpreted in…
Mean-field SDE driven by a fractional Brownian motion and related stochastic control problem
Rainer Buckdahn, Shuai Jing
We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter and a related stochastic control problem.…
Mean-Field Backward Stochastic Differential Equations and Related Partial Differential Equations
Rainer Buckdahn, Juan Li, Shige Peng
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as lim…
Uniqueness of solution to scalar BSDEs with -integrable terminal values
Rainer Buckdahn, Ying Hu, Shanjian Tang
In [4], the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) if the terminal value is $L\exp{\left(μ\sqrt{2\log{(…
Existence of an Optimal Control for Stochastic Systems with Nonlinear Cost Functional
Rainer Buckdahn, Boubakeur Labed, Catherine Rainer +1
We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled ba…