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 sum of non-independent lognormal random variables. Approximations for such sums, based on the concept of comonotonicity, have been proposed in Dhaene et al. (2002a,b). These approximations will be compared 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 lower bound approximation outperforms the two classical approximations.Approximation; Choice; Comonotonicity; Criteria; Decision; Distribution; Dual theory; Lognormal; Market; Moment matching; Optimal; Order; Portfolio; Problems; Random variables; Reciprocal gamma; Research; Risk; Risk measure; Selection; Simulation; Theory; Time; Value; Variables;