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

Vanduffel, Steven; Dhaene, Jan; Hoedemakers, Tom

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

North American Actuarial Journal, Vol. 9, No. 4, pp. 71-82, 2009

16 Pages Posted: 18 Mar 2009

See all articles by Steven Vanduffel

Tom Hoedemakers

KU Leuven - Faculty of Business and Economics (FEB)

Date Written: March 14, 2009

Abstract

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 "maximal variance" 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 "maximal variance" lower bound approximation outperforms the other approximations.

Keywords: Lognormal, Sum of random variables, Reciprocal Gamma, Annuities, Value-at-Risk

Suggested Citation: Suggested Citation

Vanduffel, Steven and Dhaene, Jan and Hoedemakers, Tom, Comparing Approximations for Risk Measures of Sums of Non-Independent Lognormal Random Variables (March 14, 2009). North American Actuarial Journal, Vol. 9, No. 4, pp. 71-82, 2009 , Available at SSRN: https://ssrn.com/abstract=1359496