Comparing Approximations for Risk Measures of Sums of Nonindependent Lognormal Random Variables |
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| Authors: | Steven Vanduffel PhD Tom Hoedemakers PhD Jan Dhaene PhD |
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| Institution: | 1. Postdoctoral Researcher at the Faculty of Economics and Econometrics of the Universiteit van Amsterdam , Roeterstraat 11 , 1018 WB Amsterdam , The Netherlands;2. Applied Economics of the Katholieke Universiteit Leuven , Naamsestraat 69, B-3000, Leuven;3. Fortis Central Risk Management , (Belgium);4. Faculty of Applied Economics of the Katholieke Universiteit Leuven , Naamsestraat 69 , B-3000, Leuven , Belgium;5. University Center of Statistics , W. de Croylaan 54, 3001 Heverlee , Belgium;6. The Faculty of Economics and Econometrics of the Universiteit van Amsterdam , Roeterstraat 11 , 1018 WB Amsterdam , Netherlands;7. Applied Economics of the Katholieke Universiteit Leuven , Naamsestraat 69, B-3000 , Leuven , Belgium |
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| Abstract: | 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 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 approximations. We find that for a wide range of parameter values the comonotonic “maximal variance” lower bound approximation outperforms the other approximations. |
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