Elliptical Distributions: Properties and Applications

This lecture explores elliptical distributions, including multivariate normal mixtures, variance mixtures, and mean-variance mixtures. Properties such as linear combinations, marginal distributions, and conditional distributions are discussed. The lecture also covers the construction of spherical samples, convolutions, density, and quadratic forms. The instructor emphasizes the preservation of properties from the multivariate normal distribution. Applications in risk management and the importance of elliptical distributions over multivariate normality are highlighted.