Comonotonic and moment matching approximations for sums of lognormal random variables
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摘要
This paper develops step-weighted distribution and demonstrates how to construct comonotonic and moment-matching approximations for sums of lognormal random variables. It shows that the proposed approximations achieve performance comparable to classical comonotonic methods in most cases, while offering improved accuracy in the right tail of the distribution, which is crucial for risk measures. A new step-weighting theory is introduced, including definitions, properties, and risk measures (VaR, TVaR, stop-loss) for step-weighted distributions, with further results on their behavior under comonotonic summation. The core contribution is a framework that yields comonotonic sums that match moments up to a given order, enabling tractable computation of distortion risk measures and tail risks for sums of continuous random variables, including sums of lognormals [page::1]
