Konferenz: Special Talk


The challenge of understanding and modeling dependence

{{_Ltalk:R}} Prof. Dr. Ashkan Nikeghbali
Datum: 07.05.14   Zeit: 10.15 - 11.00   Raum: Y10G03/04

The framework of sums of independent random variables is well understood with central limit theorems, local limit theorems, large deviations, distributional approximations and rates of convergence, etc. In practice, especially in financial modeling (e.g. popular models for credit loss portfolios), it is admitted that the independence assumption is not a realistic one, and the models that are proposed attempt to go beyond by introducing some dependence assumption (e.g. conditional independence, copulas, etc.), in such a way that at least some of the classical limit theorems we have just mentioned could still be derived. I will outline that the same challenge of understanding dependency is in fact encountered in various other places, such as in the study of the distribution of prime divisors of integer numbers, in the study of value distribution of the Riemann zeta function (which can be viewed as one of the most popular and mysterious mathematical objects), in random matr ix theory, in the distribution of cycles of random permutations, in statistical mechanics, in the study of random graphs, in asymptotic representation theory, etc. I will then introduce one framework, called mod-phi convergence, that I have developed over the past years with various collaborators, to tackle some of the problems encountered in the above mentioned areas. The goal of the talk will be to show how this new framework can potentially bring many new insights for some popular models form of mathematical finance which are based on sums of (dependent) random variables.