Correlated lognormal random sum (CLRS) is random sum,      when  are correlated and the distribution of  given  is multivariate lognormal. This paper discusses the approximation distribution for CLRS. The approximation percentile, mean and variance of CLRS are also discussed. Monte Carlo simulation is conducted to investigate the approximations. The simulation results show that the approximation distribution, percentile, mean and variance of CLRS are valid and good approximations.

correlated random sum, multivariate lognormal distribution, moment generating function, Gauss-Hermite expansion, Monte Carlo simulation.