Work

Law of large numbers for m-dependent random vectors under sublinear expectations

Year: 2024

Type: article

Abstract: Sublinear expectation relaxes the linear property of classical expectation to subadditivity and positive homogeneity, which can be expressed as $ \mathbb{E}(\cdot)=\sup_{\theta\in\Theta}E_{\theta}(\cdot) $ for a certain set of linear expectations $ \{E_{\theta}:\theta\in\Theta\} $. Such a framework can capture the uncertainty and facilitate a robust method of measuring risk loss reasonably. This study established a law of large numbers for m-dependent random vectors within the framework of sublinear expectation. Consequently, the corresponding explicit rate of convergence were derived. The results of this study can be considered as an extension of the Peng’s law of large numbers [22].

Source: Probability Uncertainty and Quantitative Risk

DOI: 10.3934/puqr.2025001

Authors: Mingcong Wu, Guanghui Cheng

Institutions: Southwestern University of Finance and Economics, Guangzhou University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Funders: National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province

Award: G4175398193