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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 classic insurance risk model and its many generalized risk models all assume the moment when the ruin probability is the negative for the first time in the study of bankruptcy probability. However, in the insurance practice, when the surplus is less than the minimum tolerable income, insurance It is very difficult for the company to operate or adjust the business strategy.On the basis of defining bankruptcy as the moment when the surplus is less than the minimum tolerable income, a dual COX risk model with disturbance and premium random collection is established, and by using the martingale theory, Study the nature of its final ruin probability and Lundberg-type inequality.