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Sums of Dependent Lognormal Random Variables: Asymptotics and Simulation

by Søren Asmussen and Leonardo Rojas-Nandayapa
Research Reports Number 469 (January 2006)
Let $(Y_1,\dots,Y_n)$ have a joint $n$-dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let $X_i=\e^{Y_i}$, $S_n=$ $X_1+\dots+X_n$. The asymptotics of $\mathbb{P}(S_n>x)$ as $n\to\infty$ is shown to be the same as for the independent case with the same lognormal marginals. Further, a number of simulation algorithms based on conditional Monte Carlo ideas are suggested and their efficiency properties studied.
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This primarily serves as Thiele Research Reports number 1-2006, but was also published in Research Reports