A brief introduction to copulas and related problems

SIAM Student Seminar
Friday, April 2, 2010 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 255
Ruodu Wang – School of Mathematics, Georgia Tech
Linwei Xin
A copula C of n arbitrary random variables X_1, ..., X_n contains all the information about their dependence. First I will briefly introduce the definition, basic properties and elementary examples of copulas, as well as Sklar's Theorem (1959). Then I will present a family of multivariate copulas whose marginal copula belongs to a family of extreme copulas. Finally I will discuss a minimization problem related to copula, which is still open. The talk should be easy to understand for all level audience who have knowledge of basic probability theory