The Multi-dimensional Ruin Probability With Heavy-tailed Distribution

The distribution theory is one of important theory of probability, while the heavy tail distribution is one of the most important parts of the theory of distribution . In the modern insurance actuary, the nonnegative random variable usually assumed to be heavy tailed. In recent years, many researcher have conducted this problem and obtained many important results, and successfully used these results in finance and insurance. A vast amount of papers has been published on the issue of the ruin probability with heavy-tailed distribution, but the problem of multi-dimensional ruin probability under the heavy tail distribution has very few papers although it has very important practical significance. In the fields of financial insurance ,the interest rate as if has little in a short time, but in the long run, the fluctuation of interest rate is actually has quite profound affects to the insurance business. Therefore, it is necessary to study the multi-dimensional ruin probability with financial risk dominates the insurance risk. What we need to point out is the ruin probability that we defined is refers to the probability that insurance company's gross profit is smaller than 0, this does not means??t the insurance company will be ruin, in fact, the bankruptcy of insurance company may be occurs many years late, because the Insurance company may be continue to add-on funds to maintain the operation, but it is an very important information for the insurance company's finance early warning system The main results of this paper can be summarized as follows: 1.there are some characters about the product and the linear combination of the heavy-tailed distribution are investigated, and with the aid of the random variable's Matuszewska moment, the multi-dimensional ruin probability is estimated when the original capital tends to infinite .2. Given the multi-dimensional ruin probability estimate under the case that the insurance risk dominates financial risk and financial risk dominates the insurance risk respectively.the results we obtained have extended the related conclusion of Tang (2003) and RogerJ.A.Leaevn.