| Uniform asymptotics for the fnite-time ruin probabilities of two kinds of nonstan-dard n-dimensional renewal risk models with difusion generated by Brownian motionsand constant interest forces are considered by this paper. In one of models, n classesof claims have diferent arrival times. In the anther model, n classes of claims havethe same arrival times. In both models, the classes of claim sizes are all upper tailasymptotically independent and their distributions belong to the intersection of thelong-tailed distribution class and the dominatedly-vary-tailed distribution class, andthe inter-arrival times follow a widely lower orthant dependence structure.About two kinds of nonstandard n-dimensional renewal risk models in this paper,one of models can be seen as that insurance company has n-kinds of insurance thattheir claims have diferent arrival times. Another model can be seen as that insurancecompany has n-kinds of insurance that their claims have the same arrival times. Inthis paper, we focus on three kinds of uniform asymptotics for the fnite-time ruinprobabilities. We defne three kinds of nonstandard n-dimensional ruin times. One ofruin times represent the frst time when all of the surplus have ever become negative.One of ruin times represent the frst time when one of the surplus have ever becomenegative. One of ruin times represent the frst time when the sum of the surplusbecomes negative. For the above three ruin times, we defne the corresponding ruinprobabilities. At the end, we obtain the three kinds of uniform asymptotics for thefnite-time ruin probabilities.According to contents, the thesis is divided into fve sections. In Chapter one, weintroduce two kinds of models which are investigated by this paper. In Chapter two, weintroduce some defnitions and the background of the defnitions. The third Chapterdescribes the main results. The forth Chapter gives some lemmas. The proof of resultsis given in Chapter fve. |
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