An elementary proof of Peng’s central limit theorem under sub-linear expectations

Zengjing Chen () and Ziwu Zhang
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Zengjing Chen: Department of Mathematics, Shandong University, 27 Shanda Nan Road, Jinan Shandong, China
Ziwu Zhang: Department of Mathematics, Shandong University, 27 Shanda Nan Road, Jinan Shandong, China

International Journal of Financial Engineering (IJFE), 2020, vol. 07, issue 02, 1-15

Abstract: Motivated by studies in mathematical finance, S. Peng established a central limit theorem (CLT) under sub-linear expectations by using partial differential equations (PDEs). In this paper, we provide a novel proof of Peng’s CLT in the frame of sub-linear expectation. Our method is not only elementary in the sense that it does not use PDEs, but also more applicable because we only require the random variables to satisfy a reasonable condition which coincides with the classical Lindeberg’s condition when the sub-linear expectation reduces to a linear expectation.

Keywords: Nonlinear expectation; capacity; central limit theorem (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S2424786320500206

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