A note on proximity of distributions in terms of coinciding moments. (Q1412438)

The aim of this article is to obtain a uniform approximation of a distribution function for which is considered to be known a finite set of its moments. The author introduces a bound on the absolute difference between two distributions having a determined moment problem and sharing the information contents of their first few moments. Using the well-known principle of maximum entropy, the approximation process is proved to be convergent. Two particular examples illustrate the proposed (continuous and discrete) upper bounds of the two distributions in terms of their entropies. Applications in the field of (mathematical) finance (evaluation of value at risk) are suggested.