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

Let XX be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) ff. Integral expressions for the c.f. of the r.v.’s max(0,X)max(0,X) in terms of ff 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.