Precise Large Deviation For Sums Of Some Heavy-tailed Claims In A Generalized Risk Model

Large deviation is now one of the hot spots in the field of financial mathematics and actuarial. The classic issue is precise large deviation. In view of the actual condition of the insurance company, a generalized risk model is proposed in this paper. The model can be interpreted from aspect that the company makes some investment. Then we introduce some important subclasses of heavy-tailed distributions, and list three classic precise large deviation theorems. Thus, for these subclasses, we give theorems and proofs for the new model. The methods are according to the proofs in Kliiuppelberg and Mikosch, Ng et al. and Balteunas et al. We can get the asymptotic of precise large deviation, in which the asymptotic zones of extended regularly varying class and consistently varying class have small difference from the classic ones, but the upper bound of the subexponential class’ has obvious discrimination. At last we give the precise large deviation results under the Cox risk process for the classic and the generalized risk model of the three heavy-tailed subclasses.