A1395
Title: Convex bounds on sums with generalized FGM copula
Authors: Alessandro Mutti - Politecnico di Torino (Italy) [presenting]
Helene Cossette - Laval University (Canada)
Etienne Marceau - Laval University (Canada)
Patrizia Semeraro - Politecnico di Torino (Italy)
Abstract: Building on the one-to-one relationship between generalized FGM copulas and multivariate Bernoulli distributions, it is proven that the class of multivariate distributions with generalized FGM copulas is a convex polytope. Therefore, sharp bounds are found in this class for many aggregate risk measures, such as value-at-risk, expected shortfall, and entropic risk measure, by enumerating their values on the extremal points of the convex polytope. This is infeasible in high dimensions. This limitation is overcome by considering the aggregation of identically distributed risks with generalized FGM copula specified by a common parameter $p$. In this case, the analogy with the geometrical structure of the class of Bernoulli distribution allows for providing sharp analytical bounds for convex risk measures.
