Precise Large Deviations For The Sums Of Random Variables In A Variety Of Dependent Relations

In this paper,we main introduce the precise large deviations for sums of random variables in a variety of dependent relations.The first one is the precise large deviations for sums of-mixing and WUOD random variables with long-tailed distributions.The second one is the precise large deviations for discounted aggregate claims in dependent multi-risk models.In the second chapter,we investigate the precise large deviations for sums of (?)-mixing and WUOD random variables with long-tailed distributions.The asymptotic relations for non-random sum and random sum of random variables with long-tailed distributions are obtained.In the third chapter,we consider a nonstandard renewal multi-risk model where a company has n types of independent insurance contracts and each contract has some dependent claims and stochastic return.The price process of the investment portfolio is described as a geometric Levy process.When the claim size distribution belongs to the class of (?),we can get some asymptotic formulae for the tail probability of n types contracts' discounted aggregate claims and ruin probabilities,holding uniformly for some finite horizons.