Dr. Giovanni Puccetti

University of Firenze, Italy

Department of Mathematics for Decisions

Abstract:

Quantitative Risk Management often starts with a vector X of one-period loss random variables.
We introduce a general mathematical framework which interpolates between different levels of information on the distribution of X
and illustrate some basic issues on how to aggregate and risk measure the random position X. In particular, we study Risk Aggregation
under different mathematical set-ups, for different aggregating functionals and risk measures, focusing on Value-at-Risk.
We show how the theory of Mass Transportations and tools originally developed to solve so-called Monge-Kantorovich problems turn out to be useful in this context.
Finally, we introduce some new numerical integration techniques which solve some open aggregation problems and raise new interesting research issues.