Abstract: Ruin probability is the core theme of non-life insurance risk theory. Compared with the classical Cramér-Lundberg Model, the modern risk model presented by Li Zehui et al is more fully considerate for the main characteristics of non-life insurance operation and has a more suitable description to realistic insurance business. Based on the modern risk model, a more realistic situation with multiple types of insurance and aggregate risk is studied. Asymptotically equivalent estimations for ruin probability are derived when the claim sizes from different insurance types have regular-tailed distributions. It can be found that, under the conditions of multiple insurance-types with large claims, the extreme claim risk faced by the company will be determined inherently by those insurance types with the heaviest tail of claim size distributions, while the effects of other insurance types which have not too heavy distributed tails are vanished. The effectiveness of results is remarkably verified by a MATLAB numerical simulation. This work is a valuable promotion for insurance risk model study. It provides a convictive evidence for risk management and initial capital setting of practical insurance businesses with multiple insurance types.

Key words: modern risk model, multiple insurance types, ruin probability, asymptotical equivalence, regular-tailed distribution, numerical simulation