有界分红下带风险投资的复合Poisson-Geometric风险模型

A Compound Poisson-Geometric Risk Model with Risk Investment and Barrier Dividend

摘要: 在考虑了保费收入为混合保费以及保险公司将多余资本用于投资来提高其赔付能力的基础上，文章首先建立随机保费收入服从复合Poisson过程，理赔量服从复合Poisson-Geometric过程且带风险投资和分红的风险模型。然后运用全期望公式与积分变换公式，得到了该模型的期望红利现值函数满足的微–积分方程及特定分布下满足的微分方程与解析解，最后通过数值模拟和算例分析了模型关键参数对期望红利现值函数的影响，得出红利现值函数是关于初始资本、风险投资额、固定保费收入、平均保费额的增函数，是关于偏离系数、平均索赔额的减函数，验证了文章得出的结果是合理的。

Abstract: Taken into account the effects of random interference because of the premiums’ randomness and mixed premium in insurance business, and used the surplus capital to invest in order to enhance the insurance payment level. We defined the risk investment and barrier dividend risk model with interference in which the random premium income follows the compound Poisson process and the claim numbers follow a compound Poisson-Geometric process. The integral-differential equation of expectation function about expected discounted dividend payment has been given by the method of total expectation formula and integral transform. In the special case, the closed form solution of the expectation formula about cumulative dividends is obtained. Finally, to illustrate the reasonableness of the obtained theoretical results, the influence of key parameters of the model on the expected dividend present value function is analyzed by numerical simulation and examples, the present value function of dividends is an increasing function of initial capital, venture capital, fixed premium income, average premium amount, and a decreasing function of deviation coefficient and average claim amount.