Weak laws of large numbers for sublinear expectation

Zengjing Chen; Qingyang Liu; Gaofeng Zong

doi:10.3934/mcrf.2018027

Article Contents

2018, Volume 8, Issue 3&4: 637-651. Doi: 10.3934/mcrf.2018027

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Weak laws of large numbers for sublinear expectation

1.
Department of Mathematics, Shandong University, Jinan 250100, China
2.
School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Bank of Weifang, Jinan 250014, China

* Corresponding author: Gaofeng Zong
* Corresponding author: Gaofeng Zong

Received: January 2018

Revised: June 2018

Published: September 2018

This work is supported in part by the National Science Foundation of China (Grant No.11501325, No.11231005), the China Postdoctoral Science Foundation (Grant No. 2018T110706) and the Taishan Scholars Climbing Program of Shandong

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Abstract

In this paper we study the weak laws of large numbers for sublinear expectation. We prove that, without any moment condition, the weak laws of large numbers hold in the sense of convergence in capacity induced by some general sublinear expectations. For some specific sublinear expectation, for instance, mean deviation functional and one-side moment coherent risk measure, we also give weak laws of large numbers for corresponding capacity.

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Mathematics Subject Classification: Primary: 60B05, 60F05; Secondary: 60A86.

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