  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 non-negative.
