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Comparing approximations for risk measures of sums of nonindependent lognormal random variables. (English) Zbl 1215.91038

Summary: 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 by J. Dhaene et al. [Insur. Math. Econ. 31, No. 2, 3–33 (2002; Zbl 1051.62107); ibid., 133–161 (2002; Zbl 1037.62107)]. 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
62E17 Approximations to statistical distributions (nonasymptotic)
62E10 Characterization and structure theory of statistical distributions

Keywords:

lognormal; risk
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References:

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