Abstract
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.
Citation
Iosif Pinelis. "Exact lower bounds on the exponential moments of truncated random variables." J. Appl. Probab. 48 (2) 547 - 560, June 2011. https://doi.org/10.1239/jap/1308662643
Information