Filtration-consistent nonlinear expectations and related g-expectations

By F. Coquet, Ying Hu, J. Mémin, Shige Peng. 2002

276 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/9c436cd33221e094f32134b1f7bf27d8611f5f0a

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Citations in the corpus

Backward stochastic differential equations with jumps and related non-linear expectations (2006, background): “Nevertheless we cannot prove nonnegative strong version of nonnegative comparison theorem in the same way as in [3] because it relies on the continuity of process Y .”
Optimal stopping for non-linear expectations—Part I (2011, unknown): “(1)  {E[·|Ft ]}t∈[0,T ], L(1)(FT )  : the linear expectation E is a special F-expectation with domain L(1)(FT ); (2)  {Eg[·|Ft ]}t∈[0,T ], L(2)(FT )  : the g-expectation with generator g(t, z) Lipschitz in z (see [14,4] or Section 5.”
Existence and Comparisons for BSDEs in general spaces (2010, background): “It is known in discrete time [6], and under some conditions in continuous time [9], that BSDEs describe all nonlinear expectations, subject to some boundedness conditions.”
Stochastic control for a class of nonlinear kernels and applications (2015, background): “[17] that essentially all filtration consistent non-linear expectations satisfying appropriate domination properties could be represented with BSDEs (we refer the reader to [43] and [16] for more recent extensions of this result).”
Optimal stopping under ambiguity in continuous time (2013, background): “[9] mention in their Remark 2.”
Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation (2006, unknown): “Since then many results have been obtained in this subject (see, among others, [3], [4], [5], [6], [10], [11], [7], [8], [24], [25], [35], [38], [39], [41], [45]).”
Backward stochastic differential equations driven by G-Brownian motion (2012, background): “In fact it was proved that there exists a 1-1 correspondence between a set of ‘dominated’ and time-consistent nonlinear expectations and that of BSDEs (see [3]).”
A general theory of finite state Backward Stochastic Difference Equations (2008, background): “As shown in [5], in continuous time with Brownian motions, the theory of Backward Stochastic Differential Equations is an appropriate context to study these operators in general.”