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Positive-part moments via characteristic functions, and more general expressions

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  • Iosif Pinelis

    (Michigan Technological University)

Abstract

A unifying and generalizing approach to representations of the positive-part and absolute moments $${{\mathsf {E}}} X_+^p$$ E X + p and $${{\mathsf {E}}}|X|^p$$ E | X | p of a random variable X for real p in terms of the characteristic function (c.f.) of X, as well as to related representations of the c.f. of $$X_+$$ X + , generalized moments $${{\mathsf {E}}} X_+^p e^{iuX}$$ E X + p e i u X , truncated moments, and the distribution function, is provided. Existing and new representations of these kinds are all shown to stem from a single basic representation. Computational aspects of these representations are addressed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:1:d:10.1007_s10959-016-0709-1
    DOI: 10.1007/s10959-016-0709-1
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    References listed on IDEAS

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    1. 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.
    2. Iosif Pinelis, 2011. "Positive-Part Moments via the Fourier–Laplace Transform," Journal of Theoretical Probability, Springer, vol. 24(2), pages 409-421, June.
    3. Deng, Chang-Song & Schilling, René L., 2015. "On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3851-3878.
    4. 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.
    5. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.

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