NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS

By Shige Peng. 2005

162 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/ab70e864dfc4328f997cc46c87bc8c5b1ef930e1

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Citations in the corpus

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]).”
Law of large numbers and central limit theorem under nonlinear expectations (2007, background): “fundamental results in probability theory. Recently problems of model uncertainties in statistics, measures of risk and superhedging in ﬁnance motivated us to introduce, in [4] and [5] (see also [2], [3] and references herein), a new notion of sublinear expectation, called “Gexpectation”, and the re”
Nonlinear Expectations and Stochastic Calculus under Uncertainty (2010, methodology): “Using nonlinear Markovian semigroup known as Nisio’s semigroup (see Nisio (1976) [86]), Peng (2005) [98] studied the processes with Markovian properties under a nonlinear expectation.”
On representation theorem of G-expectations and paths of G-Brownian motion (2009, methodology): “regarded as a combination and extension of the original Brownian motion construction approach of Kolmogorov and the Lipschitz cylinder functions Lip(Ω) (see Section 2 for its deﬁnition) introduced in [P2] and [P3]. This permits to give a much simpler proof involving only elementary results of probab”
Dynamically Consistent Nonlinear Evaluations and Expectations (2005, result): “n [20, El Karoui et al., 1997]. Most of the results in [20] can be interpreted in the language of Eg 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. For nonlinear evaluations, see [30, Peng, 20”
A semigroup approach to nonlinear Lévy processes (2017, unknown): “The G-Brownian motion due to [17, 18] is a special case of a nonlinear Lévy process, see also Dolinsky et al.”
Nonlinear Expectations, Nonlinear Evaluations and Risk Measures (2004, background): “F. Coquet, Y. Hu J. Memin and S. Peng (2002), Filtration–consistent nonlinear expectations and related g–expectations, Probab.”
G-Lévy processes under sublinear expectations (2009, background): “ ca`dla`g functions (ωt)t∈R+, with ω0 = 0, equipped with the Skorokhod topology. The corresponding canonical process is Bt(ω) = ωtfor ω∈ Ω, t≥ 0. We deﬁne Ft:= σ{Bs: s≤ t} and F = _ t≥0 Ft. Following [20, 21, 22], for each ﬁxed T∈ [0,∞), we set Lip(FT) := {ϕ(Bt1∧T,...,Btn∧T) : n∈ N,t1,...tn∈ [0,∞),ϕ”
Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths (2008, background): “Recently, we have discovered a strong link between the framework of [24, 25, 26, 27] and the one introduced in [14].”
Random G-expectations. (2010, methodology): “xtensiontothecompletion. So far, we have studied the value function Vt =Vt(ξ) for ξ∈UCb(Ω). We now set Et(ξ) :=Vt and extend this operator to a completion of UCb(Ω) by the usual procedure (e.g., Peng [12]). The main result in this section is that the dynamic programming principle carries over to the”
Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation (2006, methodology): “This paper is organized as follows: in Section 2, we recall the framework of nonlinear expectation established in [37] and adapt it to our objective.”
Martingale characterization of G-Brownian motion (2009, methodology): “The generation of a G-Brownian motion In [11], Peng used the Markov chain to generate a nonlinear expectation.”