Weak approximation of G-expectations

Yan Dolinsky; Marcel Nutz; H. Mete Soner

doi:10.1016/j.spa.2011.09.009

Weak approximation of G-expectations

Yan Dolinsky, Marcel Nutz, H. Mete Soner

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng's G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian motion.

Original language	English (US)
Pages (from-to)	664-675
Number of pages	12
Journal	Stochastic Processes and their Applications
Volume	122
Issue number	2
DOIs	https://doi.org/10.1016/j.spa.2011.09.009
State	Published - Feb 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Keywords

G-expectation
Volatility uncertainty
Weak limit theorem

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10.1016/j.spa.2011.09.009

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title = "Weak approximation of G-expectations",

abstract = "We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng's G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian motion.",

keywords = "G-expectation, Volatility uncertainty, Weak limit theorem",

author = "Yan Dolinsky and Marcel Nutz and Soner, {H. Mete}",

note = "Funding Information: This research was supported by the European Research Council Grant 228053-FiRM , the Swiss National Science Foundation Grant PDFM2-120424/1 , the Swiss Finance Institute and the ETH Foundation .",

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AU - Nutz, Marcel

AU - Soner, H. Mete

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N2 - We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng's G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian motion.

AB - We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng's G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian motion.

KW - G-expectation

KW - Volatility uncertainty

KW - Weak limit theorem

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

Weak approximation of G-expectations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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