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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 of Applied Probability – Cambridge 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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