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MARTINgALE INEQUALITIES UNDER g-expectation AND THEIR APPLICATIONS

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Acta Mathematica Scientia 2021年第2期41卷 349-360页

作者： Hanwu LI Center for Mathematical Economics Bielefeld UniversityBielefeld 33615Germany

In this paper,we study the martingale inequalities under g-expectation and their *** this end,we introduce a new kind of random time,called g-stopping time,and then investigate the properties of a g-martingale(supermartingale)such as the optional sampling theorem and upcrossing *** the help of these properties,we can show the martingale convergence property under g-expectation.

关键词： g-expectation g-supermartingale upcrossing inequality

g-expectation of distributions

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Probability, Uncertainty and Quantitative Risk 2022年第4期7卷 385-404页

作者： Mingyu Xu Zuo Quan Xu Xun Yu Zhou School of Mathematical Sciences Fudan UniversityShanghai 200433China Department of Applied Mathematics The Hong Kong Polytechnic UniversityKowloonHong KongChina Department of Industrial Engineering and Operations Research&The Data Science Institute Columbia UniversityNew YorkNY 10027USA

We define g-expectation of a distribution as the infimum of the g-expectations of all the terminal random variables sharing that *** present two special cases for nonlinear g where the g-expectation of distributions can be explicitly *** a related problem,we introduce the notion of law-invariant g-expectation and provide its sufficient *** of application in financial dynamic portfolio choice are supplied.

关键词： BSDE g-expectation Probability distribution Cost efficiency Law-invariance Portfolio selection

A Result On the Probability Measures Dominated by g-expectation

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Acta Mathematicae Applicatae Sinica 2004年第3期20卷 507-512页

作者： LongJiang Zeng-jingChen SchoolofMathematicsandSystemSciences ShandongUniversityJinan250100China

It is proved that a probability measure is dominated by g-expectation if and only if it can be generated by girsanov transformation via a process which is uniformly bounded by μ.

关键词： Backward stochastic differential equation g-expectation conditional g-expectation girsanov transformation

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

A Converse Comparison Theorem for g-expectations

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Acta Mathematicae Applicatae Sinica 2004年第4期20卷 701-706页

作者： LongJiang SchoolofMathematicsandSystemSciences ShandongUniversityJinan250100China//DepartmentofMathematicsChinaUniversityofMiningandTechnologyXuzhou221008China

With the help of a limit property of solutions of backward stochastic differential equations(BSDEs), this paper establishes a converse comparison theorem for deterministic generators g of BSDEs under the assumption g(... 详细信息

关键词： Backward stochastic differential equation generator g-expectation converse comparison theorem

Stochastic ordering by g-expectations

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Probability, Uncertainty and Quantitative Risk 2021年第1期6卷 61-98页

作者： Sel Ly Nicolas Privault School of Physical and Mathematical Sciences Division of Mathematical SciencesNanyang Technological UniversitySingapore 637371

We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and *** approach relies on comparison results for forward-backward stochastic differential equations and on several extensions of convexity,monotonicity,and continuous dependence properties for the solutions of associated semilinear parabolic partial differential *** to contingent claim price comparison under different hedging portfolio constraints are provided.

关键词： Stochastic ordering g-expectation g-evaluation g-risk measures Forward-backward stochastic differential equations Parabolic PDEs Propagation of convexity

Extended conditional g-expectations and related stopping times

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Probability, Uncertainty and Quantitative Risk 2021年第4期6卷 369-390页

作者： Mingshang Hu Shige Peng Zhongtai Securities Institute for Financial Studies Shandong UniversityJinan 250100ShandongChina School of Mathematics Shandong UniversityJinan 250100ShandongChina

In this paper,we extend the definition of conditional g-expectation to a larger space on which the dynamical consistency still *** can consistently define,by taking the limit,the conditional g-expectation for each random variable X,which is the downward limit(respectively,upward limit)of a monotone sequence (Xi) in L_(g)^(1)(Ω).To accomplish this procedure,some careful analysis is ***,we present a suitable definition of stopping times and obtain the optional stopping *** also provide some basic and interesting properties for the extended conditional g-expectation.

关键词： g-expectation Conditional g-expectation Stopping times Optional stopping theorem

gradient estimates for nonlinear diffusion semigroups by coupling methods

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Science China Mathematics 2021年第5期64卷 1093-1108页

作者： Yongsheng Song RCSDS Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper, we obtain gradient estimates for certain nonlinear partial differential equations by coupling methods. First, we derive uniform gradient estimates for certain semi-linear PDEs based on the coupling method introduced by Wang in 2011 and the theory of backward SDEs. Then we generalize Wang's coupling to the g-expectation space and obtain gradient estimates for nonlinear diffusion semigroups, which correspond to the solutions of certain fully nonlinear PDEs.

关键词： gradient estimates coupling methods g-expectation nonlinear PDEs

On the Existence and Uniqueness of Solutions to Stochastic Differential Equations Driven by g-Brownian Motion with Integral-Lipschitz Coefficients

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 589-610页

作者： Xue-peng BAI Yi-qing LIN Institut de Recherche Mathématique de Rennes Université de Rennes1 School of Mathematics Shandong University Institut de Recherche Mathématique de Rennes Université de Rennes

In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by g-Brownian motion （gSDEs） with integral-Lipschitz coefficients.

关键词： g-Brownian motion g-expectation g-stochastic differential equations g-backward stochastic differential equations integral-Lipschitz condition