On a Class of Multivariate Mixtures of Gamma Distributions: Actuarial Applications and Estimation Via Stochastic Gradient Methods

Multivariate loss distributions have been a staple of actuarial work. This paper aims to put forth a versatile class of multivariate mixtures of gamma distributions tailored for actuarial applications. Particularly, the proposed model enjoys the merits: a) allowing for an adequate fit to a wide range of multivariate data, be it in the marginal distributions and in the dependency; b) possessing desirable distributional properties for insurance valuation and risk management; and c) can be readily implemented. Various distributional properties of the model are investigated. We propose to use stochastic gradient descent methods to estimate the model’s parameters. Numerical examples based on simulation data and real-life data are presented to exemplify the insurance applications.