A MEAN–VARIANCE BOUND FOR A THREE-PIECE LINEAR FUNCTION

Karthik Natarajan, Zhou Linyi
2007 Probability in the engineering and informational sciences (Print)  
In this note, 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.
doi:10.1017/s0269964807000356 fatcat:xqvgkgsfzbb2vc7dzq2suqg5au