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Characteristic function of the positive part of a random variable and related results, with applications

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  • Pinelis, Iosif

Abstract

Let X be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) f. Integral expressions for the c.f. of the r.v.’s max(0,X) in terms of f are given, as well as other related results. Applications to stock options and random walks are presented. In particular, a more explicit and compact form of Spitzer’s identity is obtained.

Suggested Citation

  • Pinelis, Iosif, 2015. "Characteristic function of the positive part of a random variable and related results, with applications," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 281-286.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:281-286
    DOI: 10.1016/j.spl.2015.07.031
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    References listed on IDEAS

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    1. Iosif Pinelis, 2014. "An Optimal Three-Way Stable and Monotonic Spectrum of Bounds on Quantiles: A Spectrum of Coherent Measures of Financial Risk and Economic Inequality," Risks, MDPI, vol. 2(3), pages 1-44, September.
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    Cited by:

    1. Nassim Nicholas Taleb, 2018. "How Much Data Do You Need? An Operational, Pre-Asymptotic Metric for Fat-tailedness," Papers 1802.05495, arXiv.org, revised Nov 2018.
    2. Zafar Ahmad & Reilly Browne & Rezaul Chowdhury & Rathish Das & Yushen Huang & Yimin Zhu, 2023. "Fast American Option Pricing using Nonlinear Stencils," Papers 2303.02317, arXiv.org, revised Oct 2023.
    3. Iosif Pinelis, 2018. "Positive-part moments via characteristic functions, and more general expressions," Journal of Theoretical Probability, Springer, vol. 31(1), pages 527-555, March.

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