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Inf-convolution of G-expectations

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Science China Mathematics 2010年第8期53卷 1957-1970页

作者： buckdahn rainer Laboratoire de Math'ematiques CNRS-UMR 6205Universite' de Bretagne Occidentale

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 d... 详细信息

关键词： inf-convolution G-expectation G-normal distribution G-Brownian motion

Peng's maximum principle for a stochastic control problem driven by a fractional and a standard Brownian motion

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Science China Mathematics 2014年第10期57卷 2025-2042页

作者： buckdahn rainer JING Shuai Departement de Mathematiques Universite de Bretagne Occidentale School of Mathematics Shandong University School of Management Science and Engineering Central University of Finance and Economics

We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/*** 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 *** derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case.

关键词： fractional Brownian motion stochastic control system backward stochastic differential equation variational inequality maximum principle Girsanov transformation Galtchouk-Kunita-Watanabe decomposition

Fully nonlinear stochastic and rough PDEs:Classical and viscosity solutions

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Probability, Uncertainty and Quantitative Risk 2020年第1期5卷 154-212页

作者： rainer buckdahn Christian Keller Jin Ma Jianfeng Zhang Univ Brest UMR CNRS 6205Laboratoire de Mathematiques de Bretagne AtlantiqueBrest´Franceand Shandong UniversityJinanChina Department of Mathematics University of Central FloridaOrlandoFloridaUnited States Department of Mathematics University of Southern CaliforniaLos AngelesCaliforniaUnited States

We study fully nonlinear second-order(forward)stochastic *** can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified *** the most general fully nonlinear case,we develop a local theory of classical solutions and then define viscosity solutions through smooth test *** notion of viscosity solutions is equivalent to the alternative using ***,we prove basic properties such as consistency,stability,and a partial comparison principle in the general *** 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.

关键词： Stochastic PDEs path-dependent PDEs rough PDEs rough paths viscosity solutions comparison principle functional Ito formulaˆ characteristics rough Taylor expansion

On the compensator of the default process in an information-based model

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Probability, Uncertainty and Quantitative Risk 2017年第1期2卷 230-250页

作者： Matteo Ludovico Bedini rainer buckdahn Hans-Jurgen Engelbert Numerix MilanoItaly Universite de Bretagne Occidentale BrestFrance´School of MathematicsShandong UniversityJinanShandong ProvincePeople’s Republic of China Friedrich-Schiller-Universitat Fakult¨at f¨ur Mathematik und InformatikInstitut f¨ur StochastikJena¨Germany

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.

关键词： Default time Totally inaccessible stopping time Brownian bridge on random intervals Local time Credit risk Compensator process

Special issue dedicated to Alain Bensoussan on the occasion of his 80th birthday:Preface

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Probability, Uncertainty and Quantitative Risk 2022年第3期7卷 I0003-I0004页

作者： buckdahn rainer Juan Li Shige Peng 不详

We are delighted to present this special issue of PUQR in honor of Professor Alain Bensoussan on the occasion of his 80th *** 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 *** 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.

关键词： birthday occasion Ala

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Editorial

Probability, Uncertainty and Quantitative Risk 2016年第1期1卷 108-110页

作者： Shige Peng rainer buckdahn Juan Li Shandong University Ji’nanChina Universitéde Bretagne Occidentale BrestFrance Shandong University WeihaiChina

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 *** 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 *** 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 *** we further this field,it is important to provide a forum to stimulate future development with a journal that focuses on these *** precisely。

关键词： stochastic expectation backward