FGM copulas, generalizations and actuarial applications

In this talk, I will outline recent advances on the Farlie-Gumbel-Morgenstern (FGM) family copulas. I will first present a stochastic representation of FGM copulas based on multivariate symmetric Bernoulli distributions. This one-to-one correspondence lets us derive useful properties for this family. I will then study subfamilies and generalizations of FGM copulas and construct high-dimensional copulas with few dependence parameters. Then, I will explain some actuarial applications, focusing on risk aggregation (including risk-sharing and capital allocation) and collective risk models. Finally, I will conclude with current avenues for research, including high-dimensional estimation strategies and generalizing the results to Bernstein copulas.