The Research Of Ruin Probability Of Two Kinds Of Renewal Risk Model

The main task of this paper is to study the ruin probability of two kinds ofrenewal risk model. Firstly we consider the finite time ruin probability with riskyinvestment in the renewal risk model. Secondly in the compound renewal, weconsider the precise large deviations for sums of random variables. The certifiedprocess in this paper use some mathematical tools like Ito’s lemma, law of totalexpectation, Fubini lemma, Lebesgue dominated convergence theorem, Markov’sinequality and stochastic process etc. This dissertation divides three chapters. Asfollows are main contents.Chapter1is the introduction of this paper, which introduces risk theory,especially the state of research of ruin theory, the back grounds and meaning of thispaper, heavy tailed distributions, risk mode and main research contents.Chapter2is part of renewal risk model. In this model, we consider insurancetake some surplus to invest Blacks-Scholes capital market index. When the claim sizedistribution belong to class LâŒ'D, we obtain a new uniform asymptotic formula forthe ruin probability with finite time.Chapter3is part of compound renewal risk model. We investigate the preciselarge deviations for heavy-tailed random sums and extend a general asymptoticrelation in the compound renewal risk model for consistently varying taileddistribution.The last part is summary of the whole paper, and it offers some proposals for thefuture research.