Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-25T11:16:06.401Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  22 October 2007

Karthik Natarajan  and
Zhou Linyi
Karthik Natarajan
Affiliation:
Department of MathematicsNational University of SingaporeSingapore117543 E-mail: matkbn@nus.edu.sg; minniezhou@hotmail.com
Zhou Linyi
Affiliation:
Department of MathematicsNational University of SingaporeSingapore117543 E-mail: matkbn@nus.edu.sg; minniezhou@hotmail.com
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 4 , October 2007 , pp. 611 - 621
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Gallego, G. & Moon, I. (1993). The distribution free newsboy problem: Review and extensions. Journal of the Operational Research Society 44(8): 825–834.CrossRefGoogle Scholar
2.Isii, K. (1963). On the sharpness of Chebyshev-type inequalities. Annals of the Institute of Statistical Mathematics 14: 185–197.CrossRefGoogle Scholar
3.Lo, A. (1987). Semiparametric upper bounds for options prices and expected payoffs. Journal of Financial Economics 19: 373–388.CrossRefGoogle Scholar
4.Popescu, I. (2007). Robust mean–covariance solutions for stochastic optimization and applications. Operations Research 55(1): 98–112.CrossRefGoogle Scholar
5.Rogosinsky, W.W. (1958). Moments of non-negative mass. Proceedings of the Royal Society London A 245: 1–27.Google Scholar
6.Scarf, H. (1958). A min-max solution of an inventory problem. Studies in the mathematical theory of inventory and production. Stanford, CA: Stanford University Press, pp. 201–209.Google Scholar
7.van der Vlerk, M.H. (2005). On multiple simple recourse models. Mathematical Methods of Operations Research 62(2): 225–242.CrossRefGoogle Scholar