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arXiv:1309.5928 [math.PR]AbstractReferencesReviewsResources

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

Iosif Pinelis

Published 2013-09-23, updated 2015-02-18Version 3

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.

Comments: 2 pages. Version 2: 3 pages; a formula for the c.f. of |X| and three references are added; discussion expanded; title and abstract changed; Version 3: 9 pages; the paper is completely reworked; title and abstract changed; applications are given; in particular, a more explicit and compact form of Spitzer's identity is presented
Categories: math.PR
Subjects: 60E10, 44A15, 60G50, 90B22, 91G20
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