Uniform Asymptotic For The Finite-time Ruin Probability Of A Nonstandard Risk Model With Two Classes Of Claims

It is well known that the risk theory is an important part of the actuarial math-matics. while one of the main problems of which is the asymptotic estimate for the ruin probability of an insurance company. Recently, research on the standard or classical renewal risk model, i.e. Sparre-Anderson model, has been very sophisticated. Some corresponding works can be found in Grandell(1991), Embrechts et al.(1997), Rolski et al.(1999), Asmussen(2000)and others. As the research in risk theorem is increasing-ly furthered and developed and changing in the economic and financial environment, the research approach is constantly innovated as well as the realm and direction of the subject keep extending. In the past several years, many scholars have carried out numerous worthwhile studies on the risk of the insurance, builded a lot of nonstan-dard risk model, these results help the insurance industry in healthy way, and push forward the improvement and development of the risk theorem. This paper, based on the results of Wang et al.(2011). further investigate the uniform asymptotic formula for the finite-time ruin probability when the insurance company undertake more than one type of insurance business. Without loss of generality, the paper merely considers the situation of two kinds of policies, namely two series of mutually independent but not identically distributed claim sizes, while each of them are upper tail asymptotical-ly independent and identically distributed, their inter-arrival times are WLOD with identical distribution.