This document summarizes Arthur Charpentier's presentation at the Rennes Risk Workshop in April 2015. It discusses extending concepts of risk from univariate to multivariate prospects, including characterizing attitudes to multivariate notions of increasing risk like the Rothschild-Stiglitz mean preserving increase in risk and Quiggin's monotone mean preserving increase in risk. It also generalizes the Bickel-Lehmann dispersion order to multivariate risks and examines its implications for risk sharing.