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Hyperfinite construction of G-expectation

Fadina, Tolulope and Herzberg, Frederik (2019) 'Hyperfinite construction of G-expectation.' Stochastics, 91 (1). 52 - 66. ISSN 1744-2508

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Abstract

The hyperfinite G-expectation is a nonstandard discrete analogue of G-expectation (in the sense of Robinsonian nonstandard analysis). A lifting of a continuous-time G-expectation operator is defined as a hyperfinite G-expectation which is infinitely close, in the sense of nonstandard topology, to the continuous-time G-expectation. We develop the basic theory for hyperfinite G-expectations and prove an existence theorem for liftings of (continuous-time) G-expectation. For the proof of the lifting theorem, we use a new discretization theorem for the G-expectation (also established in this paper, based on the work of Dolinsky et al. [Weak approximation of G-expectations, Stoch. Process. Appl. 122(2) (2012), pp. 664–675]).

Item Type: Article
Uncontrolled Keywords: G-expectation, volatility uncertainty, weak limit theorem, lifting theorem, nonstandard analysis, hyperfinite discretization
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 21 Oct 2020 16:25
Last Modified: 21 Oct 2020 16:25
URI: http://repository.essex.ac.uk/id/eprint/28246

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