Filtration-consistent nonlinear expectations and related g-expectations

Coquet, François; Hu, Ying; Mémin, Jean; Péng, Shigē

doi:10.1007/s004400100172

Cited by 220 publications

(275 citation statements)

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“…• Some connections between properties of the driver and those of the related conditional g-expectation have been established in [BCHM02] in the case of particular g expectations called dominated g expectations. In particular, the convexity property of the driver entails that the g-expectation is itself convex.…”

Section: Commentsmentioning

confidence: 99%

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Reflected backward stochastic differential equations and a class of non-linear dynamic pricing rule

Morlais

2012

Stochastics

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In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver g is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of g-Snell enveloppe. Then, in a second step, we relate this representation to a specific class of dynamic monetary concave functionals already introduced in a discrete time setting. This connection implies that the solution, characterized by means of non linear expectations, has again the time consistency property.

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Section: Commentsmentioning

confidence: 99%

“…The proof of the existence of the decomposition is divided in three mains steps: those steps consist in following the same scheme than in the proof of Theorem 4.3 in [BBHPS03] or also in [BCHM02] (for dominated g expectations). Many computations are standard and, for sake of completeness, we provide the outline of the proofs.…”

Section: Proof Of Theoremmentioning

confidence: 99%

Reflected backward stochastic differential equations and a class of non-linear dynamic pricing rule

Morlais

2012

Stochastics

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“…Proof of Proposition 1 We can get the first part from Coquet, Hu, Mémin, and Peng (2002) Then using the uniqueness of BSDE, we have…”

Section: B Proofsmentioning

confidence: 99%

Dynamic Consistent -Maxim Expected Utility

Beißner

Lin

2015

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract We establish a class of fully nonlinear conditional expectations. Similarly to the usage of linear expectations when a probabilistic description of uncertainty is present, we observe analogue quantitative and qualitative properties. The type of nonlinearity captures the agents sentiments of optimism and pessimism in an ambiguous environment. Terms of use: Documents in EconStor mayWe then introduce an expected utility under a nonlinear expectation, and show monotonicity and continuity of utility. Risk aversion is characterized, and the properties of the certainty equivalent are discussed. Finally, we derive an Arrow-Pratt approximation of the static certainty equivalent and investigate the dynamic version via recursive equations.

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“…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]). In [37] (see also [36]), we have constructed a kind of filtration-consistent nonlinear expectations through the so-called nonlinear Markov chain.…”

Section: Introductionmentioning

confidence: 99%

A Girsanov Type Theorem Under G-Framework

Hao

Zhang

2011

Stochastic Analysis and Applications

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Summary. We introduce a notion of nonlinear expectation -G-expectationgenerated by a nonlinear heat equation with a given infinitesimal generator G. We first discuss the notion of G-standard normal distribution. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a G-Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Itô's type with respect to our G-Brownian motion and derive the related Itô's formula. We have also given the existence and uniqueness of stochastic differential equation under our G-expectation. As compared with our previous framework of g-expectations, the theory of G-expectation is intrinsic in the sense that it is not based on a given (linear) probability space.

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Filtration-consistent nonlinear expectations and related g-expectations

Cited by 220 publications

References 10 publications

Reflected backward stochastic differential equations and a class of non-linear dynamic pricing rule

Reflected backward stochastic differential equations and a class of non-linear dynamic pricing rule

Dynamic Consistent -Maxim Expected Utility

A Girsanov Type Theorem Under G-Framework

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