Аннотация:We study an asymptotic behavior of the ruin
probability
\[
P(\max_{t\in\lbrack0,T]}Q_{n}(t)>x_{T}),
\]
$t=0,1,2,...,$ for $T=0$ and large $x=x_{0}$ (instant ruin probability) and
for large both $T$ and $x_{T}$ (global ruin probability). The random process
$Q_{n}(t)$ models portfolio $Q_{n}(t)=\sum_{i=1}^{n}\lambda_{i}X_{i}(t),$
where $X_{i}(t),i=1,...,n,$ are independent random sequences, they can be
interpreted as the financial loss amount in time claimed from the $i$th direct
insurer or as reliability index of components of a technical system. Weights
$\lambda_{i},$ $i=1,...n,$ are the proportionality factors of the risks being
shared. It is assumed that the risks $X_{i}(t)$, $i=1,...,n,$ are Weibull like
in a sense that they are similar to Weibull ones in terms of the probability
of producing large values.