Title: Copulas products in completely specfied factor models
Authors: Jonathan Ansari - University of Freiburg (Germany) [presenting]
Ludger Ruschendorf - University of Freiburg (Germany)
Abstract: A completely specified factor model for a risk vector $X = (X_1 ,...,X_d)$ is considered where the joint distributions of the components of $X$ with a risk factor $Z$ and the conditional distributions of $X$ given $Z=z$ are specified. We extend the notion of *-product of-copulas as introduced for $d=2$ and continuous factor distribution previously to the multivariate and discontinuous case. We give a Sklar-type representation theorem for factor models showing that these *-products determine the copula of a completely specified factor model. We investigate in detail the approximation, transformation, and ordering properties of *-products and, based on them, derive general orthant ordering results for completely specified factor models in dependence on their specifications. In particular, we develop tools to derive worst-case distributions in relevant subclasses of completely specified factor models.