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| 1 | Peng's maximum principle for a stochastic control problem driven by a fractional and a standard Brownian motion显示文摘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 to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion.We derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case. | BUCKDAHN Rainer JING Shuai | 2014 | Science China Mathematics2014，57，10： | 1 |
| 2 | Inf-convolution of G-expectations显示文摘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-expectations and the infconvolution of drivers G. | BUCKDAHN Rainer | 2010 | Science China Mathematics2010，53，8： | 1 |
| 3 | Skorohod stochastic differential equations of diffusion type显示文摘 | Rainer Buckdahn | 1992 | Probability Theory and Related Fields1992，，3： | 1 |
| 4 | Linear skorohod stochastic differential equations显示文摘 | Rainer Buckdahn | 1991 | Probability Theory and Related Fields1991，，2： | 1 |
| 5 | Stochastic Differential Games with Reflection and Related Obstacle Problems for Isaacs Equations显示文摘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(RBSDEs) .We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way.Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bellman-Isaacs equations with obstacles,respectively.The method differs significantly from those used for control problems with reflection,with new techniques developed of interest on its own.Further,we also prove a new estimate for RBSDEs being sharper than that in the paper of El Karoui,Kapoudjian,Pardoux,Peng and Quenez(1997) ,which turns out to be very useful because it allows us to estimate the L p-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations.We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle. | Rainer BUCKDAHN | 2011 | Acta Mathematicae Applicatae Sinica2011，27，4： | 0 |
| 6 | Fully nonlinear stochastic and rough PDEs:Classical and viscosity solutions显示文摘We study fully nonlinear second-order(forward)stochastic PDEs.They can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified framework.For the most general fully nonlinear case,we develop a local theory of classical solutions and then define viscosity solutions through smooth test functions.Our notion of viscosity solutions is equivalent to the alternative using semi-jets.Next,we prove basic properties such as consistency,stability,and a partial comparison principle in the general setting.If the diffusion coefficient is semilinear(i.e,linear in the gradient of the solution and nonlinear in the solution;the drift can still be fully nonlinear),we establish a complete theory,including global existence and a comparison principle. | Rainer Buckdahn Christian Keller Jin Ma Jianfeng Zhang | 2020 | Probability, Uncertainty and Quantitative Risk2020，5，1： | 0 |
| 7 | On the compensator of the default process in an information-based model显示文摘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 of its compensator in a framework where the flow of market information on the default is modelled explicitly with a Brownian bridge between 0 and 0 on a random time interval. | Matteo Ludovico Bedini Rainer Buckdahn Hans-Jurgen Engelbert | 2017 | Probability, Uncertainty and Quantitative Risk2017，2，1： | 0 |
| 8 | Editorial显示文摘Dear All,It is with great pleasure that we welcome you to the first issue of our journal,PUQR–Probability,Uncertainty and Quantitative Risk,a peer-reviewed openaccess journal.Considering its recent and very dynamic development,the theory of backward stochastic differential equations has attracted many researchers,with its vast field of applications in stochastic control,games,finance,and deterministic and stochastic partial differential equations.This has spurred the development of new areas for research such as nonlinear dynamic expectation theory,e.g.,g and G-expectation,and path-dependent partial differential equations,while also finding new applications for problems of ambiguity,uncertainty,quantitative risk,and recursive utility in finance and economics.As we further this field,it is important to provide a forum to stimulate future development with a journal that focuses on these topics.More precisely。 | Shige Peng Rainer Buckdahn Juan Li | 2016 | Probability, Uncertainty and Quantitative Risk2016，1，1： | 0 |
| 9 | Special issue dedicated to Alain Bensoussan on the occasion of his 80th birthday:Preface显示文摘We are delighted to present this special issue of PUQR in honor of Professor Alain Bensoussan on the occasion of his 80th birthday.While this birthday provides a good opportunity to celebrate the life and the successes of an outstanding researcher,the COVID-19 epidemic has made it hard for a normal meeting.We hope that this special issue of collected papers will nevertheless provide a lasting mark for his birthday and express the appreciation and best wishes to Alain Bensoussan,from his colleagues and former students,from his co-authors and co-co-authors around the world,for a long life in good health and creative power. | Buckdahn Rainer Juan Li Shige Peng | 2022 | Probability, Uncertainty and Quantitative Risk2022，7，3： | 0 |
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