【作者】 徐娜；

【导师】 赵明清；

【作者基本信息】 山东科技大学 ， 应用数学， 2008， 硕士

【摘要】 作为一种新型的寿险产品,分红保险因其自身具备的优点,受到了国内外消费者的青睐,许多保险公司也将其作为主打产品,得到了很高的保费收入。但是,分红保险也的确存在着一些问题,因此这也就成为了专家学者研究的热点之一。分红问题是由De finetti在1957年首次提出的,Gerber和Shiu等学者对此进行了深入的研究。本文在已有研究成果的基础上,主要讨论了以下两种分红保险模型:第一种是Threshold红利策略下带利率的风险模型。之所以引入利率因素,是因为随着我国利率的市场化,利率的波动带来了一系列的利率风险问题,利率风险对分红保险产品的影响不容忽视。在Threshold红利策略下,若保险公司的盈余不高于给定水平b,则不进行红利支付;若保险公司的盈余达到给定水平b,则以速率a+δb（a≤c）支付红利,其中δ是利息力。本文得到了这种模型下的折扣罚金函数满足的积分微分方程,以及方程的解,还得到了红利付款的期望现值函数满足的积分微分方程。第二种是线性红利界限下的保费随机收取的风险模型。经典风险模型中保费的收取是按单位时间进行的,而现实中保费的收取应该是随机的,因此这一部分将保费的收取次数看作是一泊松过程,使模型更加具有现实性。在此模型中设定一个线性红利界限y_t=6+at,其中b为初值（u≤b）,a为递增速率（0＜a＜λ₁p₁）。这样,只要盈余在红利界限以下便不发放红利,一旦盈余超过红利界限便发放红利。本文得到了此模型的红利付款期望现值函数和折扣罚金函数满足的积分微分方程。更多还原

【Abstract】 As a kind of new life insurance product,participating insurance has its own advantages and thus is welcomed by the consumers home and abroad.Many insurance companies take it as their main service product,and get high premiums.But on the other hand,participating insurance has some problems and so it becomes one of the hot topics experts study.Participating insurance was first put forward by De finetti in 1957,and scholars such as Gerber and Shiu have made deep research.On the base of previous researches,this thesis studies two models of participating insurance:One is the risk model with interest and a Threshold dividend strategy.The reason why the factor of interest rate is introduced is that,since the interest rate was determined by the market, while the risk of interest rate has significant impact on participating insurance products.Under the Threshold dividend strategy,if the surplus of an insurance company is not more than a given level b,then the dividends are not paid;On the other hand,if the surplus reaches the given level b,then the dividends are paid by this formula:a +δb（a＝c ）,δis the interest force.This thesis gets the integro-differential equations for the Gerber-Shiu discounted penalty function,the solve of the equations,and also gets the integro-differential equations for the expectation present value function of dividend payments.The second model is the risk model with stochastic premium and linear dividend barrier. In the classical risk model,the premium is collected on unite time basis,but in reality,the collecting of premiums should be random,so in this part set the times of collecting premiums as a Poisson process,and make the model more realistic.In this model,set up a linear dividend barriery,=b+at,where b is an initial value（u≤b）,a is a speed（0＜a＜λ₁p₁）. Thus,if the surplus is less than the dividend barrier,the dividends are not paid.As long as the surplus is more than the dividend barrier,the dividends are paid.This thesis gets the integro-differential equations for the expectation present value function of dividend payments and the discounted penalty function.更多还原