Asymptotics of sums of lognormal random variables with Gaussian copula

By Søren Asmussen, Leonardo Rojas-Nandayapa. 2008

114 citations recorded by the source corpus.

Abstract Let ( Y 1 , … , 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 + ⋯ + X n . The asymptotics of P ( S n > x ) as n → ∞ are shown to be the same as for the independent case with the same lognormal marginals. In particular, for identical marginals it holds that P ( S n > x ) ∼ n P ( X 1 > x ) no matter what the correlation structure is.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e227c092c763c9aa3872742203656bbcb8c9b5e3

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In Finance

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Asymptotics for Risk Capital Allocations Based on Conditional Tail Expectation (2011, unknown): “…independence There has been a particular interest in understanding the tail behavior of the sum of asymptotically independent random variables with heavy tails (see Albrecher et al., 2006, Ko and Tang, 2008, Asmussen and Rojas-Nandayapa, 2008, Geluk and Tang, 2009, and Mitra and Resnick, 2009).”
Tail behavior of sums and differences of log-normal random variables (2013, background): “MR2329800 [4] Asmussen, S., Blanchet, J., Juneja, S. and Rojas-Nandayapa, L. (2011).”
Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables (2009, background): “Recently, Asmussen and Rojas-Nandayapa [4] studied the tail probability Pr(Sn > x) for a special case with dependent lognormal marginals, i.”