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1 results

  • Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

  • Part of
  • Iosif Pinelis
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 2 / June 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 547-560
    Print publication:
    June 2011
    • Article
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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.