A mean-variance bound for a three-piece linear function

Abstract

In this article, we derive a tight closed-form upper bound on the expected value of a three-piece linear convex function E[max.(0, X, mX - z)] given the mean μ and the variance σ2 of the random variable X. The bound is an extension of the well-known mean-variance bound for E[max(0, X)]. An application of the bound to price the strangle option in finance is provided. © 2007 Cambridge University Press.