The Lognormal Random Multivariate

For decades the lognormal random variable has been widely used by actuaries to analyze heavy-tailed insurance losses. More recently, especially since ERM and Solvency II, actuaries have had to solve problems involving the interworking of many heavy-tailed risks. Solutions to some of these problems may involve the relatively unknown extension of the lognormal into the multivariate realm. The purpose of this paper is present the basic theory of the lognormal random multivariate.

Keywords: lognormal, multivariate, moment generating function, positive-definite