Jianxi Su
Purdue University
Title
Some results of the multivariate truncated normal distributions with actuarial applications in view
Abstract
The multivariate normal distributions have been widely advocated as an elegant yet flexible model, which uses a simple covariance matrix parameter to capture the intricate dependence involved in high-dimensional data. However, insurance loss random variables are often assumed to be non-negative. Thereby, the multivariate normal distributions must be properly truncated to be adopted in insurance applications. In this presentation, we are going to review some fundamental statistics properties of the multivariate truncated normal distributions, including their independence, non-steepness and maximum likelihood estimation properties. For actuarial applications, we propose an efficient numeric algorithm to compute the tail-based risk functionals for the multivariate truncated normal distributions.
