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Tail approximation for reinsurance portfolios of Gaussian-like risks. (English) Zbl 1398.62294
Summary: We consider two different portfolios of proportional reinsurance of the same pool of risks. This contribution is concerned with Gaussian-like risks, which means that for large values the survival function of such risks is, up to a multiplier, the same as that of a standard Gaussian risk. We establish the tail asymptotic behavior of the total loss of each of the reinsurance portfolios and determine also the relation between randomly scaled Gaussian-like portfolios and unscaled ones. Further, we show that jointly two portfolios of Gaussian-like risks exhibit asymptotic independence and their weak tail dependence coefficient is nonnegative.

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
62G20 Asymptotic properties of nonparametric inference
62G32 Statistics of extreme values; tail inference
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