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Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

Exact Lower Bounds on the Exponential Moments of Truncated Random Variables Exact lower bounds on the exponential moments of min(y, X) and X 1{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 X 1{X < y} are demonstrated. An application to option pricing is given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Probability Cambridge University Press

Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

Journal of Applied Probability , Volume 48 (2): 14 – Jul 14, 2016

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References (30)

Publisher
Cambridge University Press
Copyright
Copyright © Applied Probability Trust 2011 
ISSN
1475-6072
eISSN
0021-9002
DOI
10.1239/jap/1308662643
Publisher site
See Article on Publisher Site

Abstract

Exact lower bounds on the exponential moments of min(y, X) and X 1{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 X 1{X < y} are demonstrated. An application to option pricing is given.

Journal

Journal of Applied ProbabilityCambridge University Press

Published: Jul 14, 2016

Keywords: Exponential moments; exact lower bounds; Winsorization; truncation; large deviations; nonuniform Berry-Esseen bounds; Cramér tilt transform; option pricing; 60E15; 60E10; 60F10; 60F05

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