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Density approximations and VaR computation for compound Poisson-lognormal distributions. (English) Zbl 1364.62038
Summary: Parametric approximations of the compound Poisson-lognormal distribution are developed and used to compute Value-at-Risk (VaR). As guidelines for finding an approximation, the skewness-kurtosis space and the tail behavior are considered. The Generalized Beta distribution of the second kind (GB2) and a mixture of lognormals are found to provide a good fit. In certain cases, the GB2 can be estimated by moment-matching, thus providing a simulation-free procedure for VaR computation. For confidence levels larger than 99%, extreme value theory approaches are developed. According to extensive Monte Carlo evidence, the proposed approximations are more efficient than crude Monte Carlo.

62E17 Approximations to statistical distributions (nonasymptotic)
62P05 Applications of statistics to actuarial sciences and financial mathematics
evir; nleqslv; QRM
Full Text: DOI
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