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Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

Part of: Limit theorems Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Iosif Pinelis
Iosif Pinelis*
Affiliation:
Michigan Technological University
*
∗Postal address: Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA. Email address: [email protected]
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Abstract

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Exact lower bounds on the exponential moments of min(y, X) and X1{X < y} are provided given the first two moments of a random variable X. These bounds are useful in work on large deviation probabilities and nonuniform Berry-Esseen bounds, when the Cramér tilt transform may be employed. Asymptotic properties of these lower bounds are presented. Comparative advantages of the so-called Winsorization min(y, X) over the truncation X1{X < y} are demonstrated. An application to option pricing is given.

Keywords

Exponential momentsexact lower boundsWinsorizationtruncationlarge deviationsnonuniform Berry-Esseen boundsCramér tilt transformoption pricing

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60E10: Characteristic functions; other transforms 60F10: Large deviations 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 2 , June 2011 , pp. 547 - 560
Copyright
Copyright © Applied Probability Trust 2011 

Footnotes

Supported by NSF grant DMS-0805946.

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