Closed form solution of correlation in doubly truncated or censored sample of bivariate log-normal distribution

In this study we present a closed form solution to the moments and, in particular, correlation of two log-normally distributed random variables, when the underlying log-normal distribution is potentially truncated or censored at both tails. The closed form solution that we derive also covers the cases where one tail is truncated and the other is censored. Throughout the derivations we further assume that the moments of the unconstrained bivariate log-normal distribution are known.