Application of Chebyshev Inequality and Central Limit Theorem in Financial Field and Comparison of their Advantages and Disadvantages

Yulin Huang ()
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Yulin Huang: Xi’an Jiaotong University

A chapter in Proceedings of the 2025 5th International Conference on Enterprise Management and Economic Development (ICEMED 2025), 2025, pp 1023-1029 from Springer

Abstract: Abstract This paper discusses the application of Chebyshev inequality and Central limit theorem in the field of finance and compares their advantages and disadvantages. Through theoretical analysis and empirical research, this paper first introduces the basic principles and derivation process of the two statistical methods, and then applies them to the actual financial data analysis. In this study, the data of stock return rate is selected as a sample, which is estimated by Chebyshev inequality and central limit theorem respectively, and compared with the actual distribution. The results show that Chebyshev inequality provides a more conservative but reliable estimate when the distribution of financial data is unknown, while the central limit theorem provides a more accurate approximation when the sample size is large enough. This study provides important theoretical support and practical guidance for financial risk management, investment decision making and pricing of financial derivatives.

Keywords: Chebyshev inequality; Central limit theorem; Financial risk management; Investment decision; Pricing of financial derivatives; Statistical estimation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:advbcp:978-94-6463-811-0_110

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DOI: 10.2991/978-94-6463-811-0_110

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