ABSTRACT
One of the main challenges in risk management is the aggregation of individual risks. We can move the issue aside by assuming that the random variables modeling individual risks are independent or are only dependent by means of a common risk factor. The problem becomes much more involved when one wants to model fully dependent random variables. Again a classic solution is to assume that the vector of individual risks follows a multivariate normal distribution. However, all risks are not likely to be well described by a Gaussian random vector, and the normal distribution may fail to catch some features of the dependence between individual risks.
Copula functions are a statistical tool to solve the previous issue. A copula function is nothing else but the joint distribution of a vector of uniform random variables. Since it is always possible to map any random vector into a vector of uniform random variables, we are able to split the marginals and the dependence between the random variables. Therefore, a copula function represents the statistical dependence between random variables, and generalizes the concept of correlation when the random vector is not Gaussian.
