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 σ 2 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.