A Converse Comparison Theorem for BSDEs and Related Properties of g-Expectation

By P. Briand, F. Coquet, Ying Hu, J. Mémin, Shige Peng. 2000

172 citations recorded by the source corpus.

In [1], Z. Chen proved that, if for each terminal condition $\xi$, the solution of the BSDE associated to the standard parameter $(\xi, g_1)$ is equal at time $t=0$ to the solution of the BSDE associated to $(\xi, g_2)$ then we must have $g_1\equiv g_2$. This result yields a natural question: what happens in the case of an inequality in place of an equality? In this paper, we try to investigate this question and we prove some properties of ``$g$-expectation'', notion introduced by S. Peng in [8].

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f295d442c6992a679a9e2912beb5dce942260e9c

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Citations in the corpus

G -Expectation, G -Brownian Motion and Related Stochastic Calculus of Itô Type (2006, unknown): “Since then many results have been obtained in this subject (see, among others, [3], [4], [5], [6], [10], [11], [7], [8], [22], [23], [34], [38], [39], [41], [43], [24]).”
Filtration-consistent nonlinear expectations and related g-expectations (2002, background): “For more detailed views on this topic, we refer to [11], [4], [12], or [ 1 ] where some special cases are studied in depth, including the y-independent case, which will turn out to be the natural setting behind the present work.”
Convexity, translation invariance and subadditivity for g-expectations and related risk measures (2008, methodology): “3 of [3] and helps us to confirm the same necessary and sufficient conditions in [3] and [21] without the additional continuity assumption (A4).”
Optimal Stopping for Non-Linear Expectations - Part II (2011, unknown): “1 of [3], the reverse statement also holds given that almost surely, the mapping t → g(t, z) is continuous for any z ∈ Rd .”
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]).”
A general theory of finite state Backward Stochastic Difference Equations (2008, background): “o consider the reverse problem, that is to see whether, given the solutions to the BSDE, we can determine the values of the function F. A short comment on doing this is in [13], with other results in [2]. However, this is only in continous time with an underlying Brownian motion, and, as might be ex”
Nonlinear Expectations, Nonlinear Evaluations and Risk Measures (2004, background): “Our new observation is: for each p ∈ [1, 2), {zi} converges strongly in L.”
Dynamically Consistent Nonlinear Evaluations and Expectations (2005, result): “Most of the results in [20] can be interpreted in the language of E g s,t[� ]. Other recent results in g–expectations are in [ 5 ], [6], [8], [11], [12], [13], [28], [29], [30], [31], [32] where some cases are studied in depth.”
On the comparison theorem for multidimensional BSDEs (2006, unknown): “(7) This is established already in [1].”