A refinement of Bennett's inequality with applications to portfolio optimization

04/16/2018
by   Tony Jebara, et al.
0

A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully exploits information about the potentially heterogeneous mean, variance, and ceiling of each random variable. The bound is strictly sharper in the homogeneous setting and very often significantly sharper in the heterogeneous setting. The improved convergence rates are obtained by leveraging Lambert's W function. We apply the new bound in a portfolio optimization setting to allocate a budget across investments with heterogeneous returns.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

04/29/2019

Cramér-Rao-type Bound and Stam's Inequality for Discrete Random Variables

The variance and the entropy power of a continuous random variable are b...
03/29/2021

Exact converses to a reverse AM–GM inequality, with applications to sums of independent random variables and (super)martingales

For every given real value of the ratio μ:=A_X/G_X>1 of the arithmetic a...
12/19/2018

Convergence Rates for the Generalized Fréchet Mean via the Quadruple Inequality

For sets Q and Y, the generalized Fréchet mean m ∈ Q of a random varia...
12/30/2019

Iterated Jackknives and Two-Sided Variance Inequalities

We consider the variance of a function of n independent random variables...
02/18/2020

Vector Gaussian Successive Refinement With Degraded Side Information

We investigate the problem of the successive refinement for Wyner-Ziv co...
01/12/2021

A note on a confidence bound of Kuzborskij and Szepesvári

In an interesting recent work, Kuzborskij and Szepesvári derived a confi...
02/24/2021

Saturable Generalizations of Jensen's Inequality

Jensen's inequality can be thought as answering the question of how know...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.