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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zengjing Chen & Ziwu Zhang, 2020. "An elementary proof of Peng’s central limit theorem under sub-linear expectations," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-15, June.
    • Handle: RePEc:wsi:ijfexx:v:07:y:2020:i:02:n:s2424786320500206
    DOI: 10.1142/S2424786320500206
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