Lecture Series by Dr. Jonathan Ansari: Dependence Modeling – February 2024
This lecture series offers an introduction to current research topics in dependence modelling. First, basic concepts such as copulas and stochastic orders are studied. In the further course, different model classes such as *-products and Vine copulas will be discussed. Finally, the focus is on dependence measures which satisfy the basic axioms that they characterise independence and perfect directed dependence between random vectors. Special attention is given to the rank correlation recently developed by Chatterjee, which can be estimated in almost linear time and allows a model-free variable selection. These concepts find applications in model construction, for example. More generally, dependence modelling is a main topic in risk management in the finance and insurance industry, where copulas are part of the actuarial education.