An upper bound of large deviations for capacities
type: Item
instance of: scholarly article
title: An upper bound of large deviations for capacities
zbMATH Open document ID: 1407.60040
DOI: 10.1155/2014/516291
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: Up to now, most of the academic researches about the large deviation and risk theory are under the framework of the classical linear expectations. But motivated by problems of model uncertainties in statistics, measures of risk, and superhedging in finance, sublinear expectations are extensively studied. In this paper, we obtain a type of large deviation principle under the sublinear expectation. This result is a new expression of the Gärtner-Ellis theorem under the sublinear expectations which is in the classical theory of large deviations. In addition, we introduce a new process under the sublinear expectations, that is, the \(G\)-Poisson process. We give an application of our result and obtain the rate function of the compound \(G\)-Poisson process in the upper bound of large deviations for capacities. The application of our result opens a new field for the research of risk theory in the future.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 7016638
author: Xiaomin Cao
MaRDI profile type: Publication
Wikidata QID: Q59068115
full work available at URL: https://doi.org/10.1155/2014/516291
OpenAlex ID: W2045194515
cites work: Q4391441
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description: scientific article; zbMATH DE number 7016638