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A Relationship Between the Conditional g-evaluation System and the generator g and Its Applications

Acta Mathematica Sinica,English Series 2007年第8期23卷 1427-1434页

作者： Sheng Jun FAN College of Sciences China University of Mining and Technology Xuzhou 221008 P. R. China

In this paper, under the most elementary conditions on a backward stochastic differential equation （BSDE for short） introduced by Peng, a new relationship between the conditional g-evaluation system and the generator g of BSDE is obtained in the sense of ＂process＂, based on some recent results of Jiang. Moreover, as applications, two converse comparison theorems and two uniqueness theorems on the generators of BSDEs are proved.

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

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Some properties on g-evaluation and its applications to g-martingale decomposition

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Science China Mathematics 2011年第2期54卷 287-300页

作者： SONg YongSheng Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

In this article, a sublinear expectation induced by g-expectation is introduced, which is called g- evaluation for convenience. As an application, we prove that for any ξ∈ L β g (Ω T ) with some β > 1 the martingale decomposition theorem under g-expectaion holds, and that any β > 1 integrable symmetric g-martingale can be represented as an Ito integral w.r.t. g-Brownian motion. As a byproduct, we prove a regularity property for g-martingales: Any g-martingale {M t } has a quasi-continuous version.

关键词： g-expectation g-evaluation g-martingale decomposition theorem

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Dynamically Consistent Nonlinear evaluations with Their generating Functions in L^p

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Acta Mathematica Sinica,English Series 2013年第4期29卷 815-832页

作者： Feng HU School of Mathematical Sciences Qufu Normal University

In this paper, we study dynamically consistent nonlinear evaluations in Lp （1 〈 p 〈 2）. One of our aim is to obtain the following result： under a domination condition, an Ft-consistent evaluation is an Sg-evaluation in Lp. Furthermore, without the assumption that the generating function g（t, w, y, z） is continuous with respect to t, we provide some useful characterizations of an εg-evaluation by g and give some applications. These results include and extend some existing results.

关键词： Backward stochastic differential equation (BSDE) dynamically consistent nonlinear evaluation g-evaluation dynamic risk measure

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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

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