Fadina, Tolulope and Herzberg, Frederik (2019) Hyperfinite construction of G-expectation. Stochastics, 91 (1). pp. 52-66. DOI https://doi.org/10.1080/17442508.2018.1502771
Fadina, Tolulope and Herzberg, Frederik (2019) Hyperfinite construction of G-expectation. Stochastics, 91 (1). pp. 52-66. DOI https://doi.org/10.1080/17442508.2018.1502771
Fadina, Tolulope and Herzberg, Frederik (2019) Hyperfinite construction of G-expectation. Stochastics, 91 (1). pp. 52-66. DOI https://doi.org/10.1080/17442508.2018.1502771
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 |
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Uncontrolled Keywords: | G-expectation, volatility uncertainty, weak limit theorem, lifting theorem, nonstandard analysis, hyperfinite discretization |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematical Sciences, Department of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 21 Oct 2020 16:25 |
Last Modified: | 06 Jan 2022 14:16 |
URI: | http://repository.essex.ac.uk/id/eprint/28246 |
Available files
Filename: 1810.09386.pdf