Comparing Approximations for Risk Measures of Sums of Non-Independent Lognormal Random Variables

In this paper we consider different approximations for computing the distribution function or risk measures related to a discrete sum of nonindependent lognormal random variables. Comonotonic upper bound and lower bound approximations for such sums have been proposed in Dhaene et al. (2002a,b). We introduce the comonotonic quot;maximal variancequot; lower bound approximation. We also compare the comonotonic approximations with two well-known moment matching approximations: the lognormal and the reciprocal Gamma approximation. We find that for a wide range of parameter values the comonotonic quot;maximal variancequot; lower bound approximation outperforms the other approximations