容忍最小收益下带干扰的双COX风险模型

A Double COX Risk Model with Perturbation under Tolerance Smallest Income

Lundberg-Cramer经典保险风险模型及其推广后的许多风险模型在研究破产概率时都假定破产时刻为盈余过程首次取负值的时刻.但在保险实务中,当盈余低于容忍最小收益时,保险公司就很难再经营下去或需要调整经营策略.在定义盈余低于容忍最小收益时的时刻为破产时刻的基础上,建立一个带干扰且保费随机收取的双COX风险模型,利用鞅论方法,研究其最终破产概率的性质及Lundberg型不等式.

The Lundberg-Cramer classical risk model and some of its extendable risk models assume that the time of ruin is the surplus process which takes a negative value for the first time when they research ruin probability. However, in practice, insurance agent will be placed in difficult circumstances or need to adjust its business strategy when its surplus is under a limit. The first literature reference defines the limit as the tolerance smallest income. In this paper, a double COX risk model with perturbation and stochastic premium is established based on defining the time of ruin as the time when the surplus process is under the tolerance smallest income. The Lundberg＇s inequality and some quality of final ruin probability in this new model are obtained through the method of martingale.