带投资和分红策略下复合Poisson-Geometric风险模型的研究

RESEARCH ON COMPOUND POISSON-GEOMETRIC RISK MODEL WITH INVESTMENT AND DIVIDEND STRATEGIES

考虑投资和分红策略下,建立带有混合收费及索赔计数服从复合Poisson-Geometric过程的风险模型。运用全期望公式与积分变换公式,研究该模型红利付款现值期望函数满足的微积分方程和特定指数分布下满足的微分方程及解析解,通过数值模拟分析了固定保费率、初始资本、投资资产、索赔强度和红利边界对红利付款现值期望函数的影响,并分析其经济意义。

Considering investment and dividend strategies,a risk model with mixed charges and claims following a compound Poisson-Geometric process was established.By using the full expectation formula and integral transformation formula,the micro-integral equation satisfied by the dividend payment expectation function of this model and the differential equation and analytic solution satisfied under specific exponential distribution were studied.The effects of fixed premium rate,initial capital,investment assets,claim intensity and dividend boundary on the dividend payment expectation function were analyzed by numerical simulation,and their economic significance was also analyzed.