Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims

By Shige Peng. 2004

154 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/44b7332737f796cd464c371c47f1d7cca3fdb087

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Citations in the corpus

Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, background): “The first result was obtained in Coquet, Hu, Memin and Peng (2001) (see also lecture notes of a CIME course of Peng (2004a)): under an additional condition such that E is dominated by a gµ-expectation with gµ(z) = µ|z| for a large enough constant µ > 0, namely Es,t[ξ]− Es,t[ξ ′ ] ≤ E gµ s,t [ξ − ξ…”
Constructing Sublinear Expectations on Path Space (2012, background): “robability measure) can often be seen as sublinear expectations on Ω by a push-forward, that is, by taking ξto be the reward functional and P the set of possible laws of the controlled process (e.g., [14, 16]). Our starting point is a family of sets P(τ,ω) of probability measures, where τis a stoppi”
Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation (2006, background): “6 in [36] for a more general conclusion).”
A complete representation theorem for G-martingales (2012, background): “A complete representation theorem for G-martingales Shige Penga,1, Yongsheng Songb* and Jianfeng Zhangc,2 aSchool of Mathematics, Shandong University, Jinan, P.R. China; bAcademy of Mathematics and Systems Science, CAS, Beijing, P.R. China; cDepartment of Mathematics, University of Southern Californ”
A probabilistic weak formulation of mean field games and applications (2013, methodology): “This method is discussed by El Karoui and Quenez in [30], Peng in [37], and perhaps most thoroughly by Hamadene and Lepeltier in [23].”
Backward stochastic differential equations driven by G-Brownian motion (2012, background): “The notion of time-consistent fully nonlinear expectations has been established in [15, Peng2004] and [16, Peng2005].”
Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths (2008, methodology): “This situation was studied independently by [ 19 ]a nd [11] with very different approaches.”
Optimal Stopping under Nonlinear Expectation (2012, methodology): “ E∩(∩∞ i=1E c) . 4 We refer to the seminal work of Stroock and Varadhan [18] for the introduction of r.c.p.d., which is a convenient tool for proving the dynamic programming principles, see e.g. Peng [12] and Soner, Touzi, and Zhang [15]. We observe that for all L>0, the family {PL t ,t∈ [0,T]} s”
Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion (2012, background): “1 Introduction Recently, Peng systemically established a time-consistent fully nonlinear expectation theory (see [17], [18] and [23]).”
A New Central Limit Theorem under Sublinear Expectations (2008, background): “Recently problems of model uncertainties in statistics, measures of risk and superhedging in finance motivated us to introduce, in [13] and [14] (see also [11], [12] and references herein), a new notion of sublinear expectation, called “G-expectation”, and the related “G-normal distribution” (see De”
Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012, background): “[31] or [24], implies further the following dynamic programming principle:”
Random G-expectations. (2010, methodology): “The author thanks Shige Peng, Mete Soner and Nizar Touzi for stimulating discussions as well as Laurent Denis, Sebastian Herrmann and the anonymous referees for helpful comments.”
G -Expectation, G -Brownian Motion and Related Stochastic Calculus of Itô Type (2006, background): “),i.e.,a m easurable space ( ;F ) equipped with a probability m easure P becom es a standard notion which appearsin m ostpapersofprobability and m athem atical nance.”
Dual Formulation of Second Order Target Problems (2010, methodology): “In the contexts of stochastic control, which naturally uses strong formulation, some ideas have already appeared in the literature; see, for example, El Karoui and Quenez [10] and Peng [16].”
Quasi-continuous random variables and processes under the G-expectation framework (2014, methodology): “Motivated by model uncertainty in finance, Peng 2004-2005 firstly constructed a kind of dynamically consistent fully nonlinear expectations on (Ω, Lip(Ω)) by stochastic control and PDE methods (see [9, 10]).”