带有双投资和分红策略Poisson-Geometric风险模型的破产概率

Ruin probability of Poisson-Geometric risk model with double investment and dividend strategy

考虑到随机干扰因素的影响,将多余的资本进行风险投资和稳定低利率投资,以提高保险公司的赔付能力.构建了带有双投资和分红策略的随机扰动风险模型,其中保费过程、索赔过程及分红过程均为Poisson-Geometric过程.对模型的性质进行讨论,证明了盈利过程具有平稳独立增量,得到了盈余过程的数字特征.运用概率和随机过程基本理论推导调节系数满足的方程,并得到破产概率的一般表达式和Lundberg不等式.当保费、理赔和分红过程服从指数分布时,得到破产概率的具体表达式.

Considering the influence of random interference factors,the excess capital will be used for venture capital investment and stable low interest rate investment to improve the compensation ability of insurance companies.And a random disturbance risk model with dual investment and dividend strategy is constructed,in which the premium process,claim process and dividend process are the Poisson-Geometric process.The properties of the model are discussed,and it is proved that the profit process has stable independent increment,the digital characteristics of surplus process are obtained.The equation satisfied by the adjustment coefficient is deduced by using the basic theory of probability and random process,and the general expression of ruin probability and Lundberg inequality are obtained.When the premium,claim and dividend processes obey exponential distribution,the specific expression of ruin probability is obtained.