In view of the actual condition of the insurance company, a multi-risk model is proposed. The lower bound for the sums of long-tailed claims in this model is given. The proof method is based on the results of precise large deviation for long-tailed distributions.

In view of the actual condition of the insurance company, a multi-risk model is proposed. The lower and upper bounds for the sums of subexponential claims in this model are given. The proof method is based on the results of the total claim amount under subexponential class.