Random G-expectations.

By Marcel Nutz. 2010

67 citations recorded by the source corpus.

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and based on an optimal control formulation with path-dependent control sets.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/482b435cd983c827fe7de02c063b928f88187fe9

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Citations in the corpus

Note on Viscosity Solution of Path-Dependent PDE and G-Martingales (2011, background): “It also provides a new PDE formulation of G-expectations with random coefficients G (see [Nutz2010] for a formulation of stochastic calculus).”
Superreplication under Volatility Uncertainty for Measurable Claims (2012, methodology): “enerally, upper semianalytic) claims ξand a model P where the possible values of the volatility are determined by a set-valued process. Such a model of a “random G-expectation” was ﬁrst introduced in [9], as an extension of the “G-expectation” of [15, 16]. ∗Dept. of Mathematics, ETH Zurich, ariel.ne”
UTILITY MAXIMIZATION UNDER MODEL UNCERTAINTY IN DISCRETE TIME (2013, background): “The passage from the one-period markets to the original market is achieved via measurable selections and in particular the theory of lower semianalytic functions; it draws from [6, 24, 25, 33].”
Constructing Sublinear Expectations on Path Space (2012, background): “Among other improvements, we shall remove completely the uniform continuity assumption that had to be imposed on D in [13].”
Nonlinear Lévy Processes and their Characteristics (2016, background): “The present setup could be extended to a case where the set Θ is replaced by a set-valued process (t, ω) 7→ Θ(t, ω), in the spirit of the random G-expectations [15].”
Arbitrage and duality in nondominated discrete-time models (2013, methodology): “The present study is also related to the theory of nonlinear expectations and we make use of ideas developed by [43, 46] in that context.”
ROBUST UTILITY MAXIMIZATION IN NONDOMINATED MODELS WITH 2BSDE: THE UNCERTAIN VOLATILITY MODEL (2015, background): “One first step in this direction has been taken by Nutz (2013) where he defines a notion of G-expectation (which roughly corresponds to a 2BSDE with a generator equal to 0) with a stochastic domain of volatility uncertainty.”
Martingale Representation Theorem for the G-Expectation (2010, unknown): “The paper [4] also provides a dual representation of the G-expectation as the supremum of expectations over P. This duality and more generally the dynamic programming principle is generalized by Nutz [13] who considers lower and upper bounds a, athat are random processes. A probabilistic constructio”
Optimal arbitrage under model uncertainty. (2011, background): “With F ♭(t) := σ(ω(s),0≤ s≤ t), the filtration F♭ = {F (t)}0≤t<∞ is a standard system in the terminology of Parthasarathy (1967). This means that each (Ω,F ♭(t)) is isomorphic to the Borel σ-algebra on some Polish space, and that for any decreasing sequence {Aj}j∈N where each Aj is an atom of the co”
A complete representation theorem for G-martingales (2012, background): “The theory has received very strong attention in the literature in recent years, we refer to the survey paper [20] and the references therein as well as some more recent developments: [4,5,10,12,13,15,16,26], to mention a few.”
Weak approximation of G-expectations (2011, background): “The extension to a random set D is studied in [9].”