On Log-Normal Convolutions : An Analytical-Numerical Method With Applications to Economic Capital Determination

We put forward an efficient algorithm for approximating the sums of independent and lognormally distributed random variables. Namely, by merging tools from probability theory and numerical analysis, we are able to compute the cumulative distribution functions of the just-mentioned sums with any desired precision. Importantly, our algorithm is fast and can tackle equally well sums with just a few or thousands of summands. We illustrate the effectiveness of the new method in the contexts of the individual and collective risk models, aggregate economic capital determination, and economic capital allocation