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

  • Authors:

  • Karthik Natarajan;Zhou Linyi

  • Affiliations:

  • Department of MathematicsNational University of SingaporeSingapore117543 E-mail: matkbn@nus.edu.sg/ minniezhou@hotmail.com;Department of MathematicsNational University of SingaporeSingapore117543 E-mail: matkbn@nus.edu.sg/ minniezhou@hotmail.com

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2007

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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.