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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: [email protected]; [email protected]
Zhou Linyi
Affiliation:
Department of MathematicsNational University of SingaporeSingapore117543 E-mail: [email protected]; [email protected]
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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.

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

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