Lower Bounds on Large Deviation Probabilities for Sums of Independent Random Variables

2001 ◽  
pp. 277-295
Author(s):  
S. V. Nagaev
Keyword(s):  
Lower Bounds ◽  
Large Deviation ◽  
Random Variables ◽  
Independent Random Variables ◽  
Large Deviation Probabilities

scholarly journals Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

2011 ◽  
Vol 48 (02) ◽  
pp. 547-560 ◽  
Author(s):  
Iosif Pinelis
Keyword(s):  
Option Pricing ◽  
Lower Bounds ◽  
Large Deviation ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Random Variable ◽  
Exponential Moments ◽  
Comparative Advantages ◽  
Large Deviation Probabilities

Exact lower bounds on the exponential moments of min(y,X) andX1{X<y} are provided given the first two moments of a random variableX. 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 truncationX1{X<y} are demonstrated. An application to option pricing is given.

scholarly journals Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

2011 ◽  
Vol 48 (2) ◽  
pp. 547-560 ◽  
Author(s):  
Iosif Pinelis
Keyword(s):  
Option Pricing ◽  
Lower Bounds ◽  
Large Deviation ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Random Variable ◽  
Exponential Moments ◽  
Comparative Advantages ◽  
Large Deviation Probabilities

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.

scholarly journals The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables

2010 ◽  
Vol 47 (04) ◽  
pp. 908-922 ◽  
Author(s):  
Yiqing Chen ◽  
Anyue Chen ◽  
Kai W. Ng
Keyword(s):  
Law Of Large Numbers ◽  
Large Deviation ◽  
Random Variables ◽  
Renewal Theory ◽  
Independent Random Variables ◽  
Strong Law ◽  
Finite Dimensional ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
New Inequalities

A sequence of random variables is said to be extended negatively dependent (END) if the tails of its finite-dimensional distributions in the lower-left and upper-right corners are dominated by a multiple of the tails of the corresponding finite-dimensional distributions of a sequence of independent random variables with the same marginal distributions. The goal of this paper is to establish the strong law of large numbers for a sequence of END and identically distributed random variables. In doing so we derive some new inequalities of large deviation type for the sums of END and identically distributed random variables being suitably truncated. We also show applications of our main result to risk theory and renewal theory.

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