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Normal approximation for call function of m-dependent random variables with 2+δ-th moment

Author

Listed:
  • Zhang, Ting
  • Tian, Lulu
  • Qi, Tianyi

Abstract

For the call function hk(x)=max{x−k,0} with some fixed k>0, we apply Stein’s method to give the upper bounds of normal approximation under the weaker moment condition, containing both uniform and non uniform situations. Specifically, we discuss a sum of m-dependent and identically distributed random variables with weaker (2+δ)-th moment for some δ∈(0,1). Our results enable the application in call function to possess a broader field with normal approximation techniques.

Suggested Citation

  • Zhang, Ting & Tian, Lulu & Qi, Tianyi, 2026. "Normal approximation for call function of m-dependent random variables with 2+δ-th moment," Statistics & Probability Letters, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:stapro:v:227:y:2026:i:c:s0167715225001956
    DOI: 10.1016/j.spl.2025.110550
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    References listed on IDEAS

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    1. Glasserman, Paul & Suchintabandid, Sira, 2007. "Correlation expansions for CDO pricing," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1375-1398, May.
    2. Chen, Peng & Qi, Tianyi & Zhang, Ting, 2025. "Stable approximation for call function via Stein’s method," Statistics & Probability Letters, Elsevier, vol. 219(C).
    3. Suporn Jongpreechaharn & Kritsana Neammanee, 2019. "Normal approximation for call function via Stein’s method," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(14), pages 3498-3517, July.
    4. Maejima, Makoto & Sakuma, Noriyoshi, 2023. "Rates of convergence in the free central limit theorem," Statistics & Probability Letters, Elsevier, vol. 197(C).
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