ИСТИНА

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.