离散的三项分布风险模型的渐近解

Trinomial Distribution Risk Model in Discrete Setting and the Asymptotic Formulae

本文研究了离散的三项分布风险模型,在调节系数存在的前提下,借助于离散更新方程的一个极限定理,对于充分大的初始盈余给出了最终破产概率、破产前一刻的盈余和破产时赤字的概率的渐近解．其结果可以在离散的多项分布风险模型中得到推广．

The trinomial distribution risk model in discrete setting is explored in this paper.Under the assumption for existence of the adjustment coefficient, the asymptotic formulae for the ultimate ruin probability, the probabilities of surplus immediately before ruin and the deficit at ruin are given for sufficiently large initial surlus by means of a discrete key renewal limit theorem. The results can be generalized in the multinomial distribution risk model.