This note deals with an insurance company with multiple lines of business. In the context of heavy-tailed heterogeneous claim amounts with the 1st upper-orthant tail dependence, based on the so-called k-out-of-n ruin set, we can exhibit the Radon measure mu and derive the asymptotic ruin probability for some of all lines business to ruin in a finite time. One numerical example is also presented to illustrate our main results.
The project was supported by the Scientific Research Funds of Huaqiao University (Grant No. 15BS312), the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University (Grant No. ZQN-PY503) and the National Natural Science Foundations of China (Grant Nos. 11171278; 11701194)