本文選題：隨機利率 + 分期付款��； 參考：《哈爾濱工程大學》2014年碩士論文

【摘要】：在實際生活中,人們可能會面臨疾病和意外事故所帶來的死亡風險,雖然個體面臨的死亡風險難以預測,但從群體角度來看,風險具有穩(wěn)定性。對保險公司來說,單個投保人的死亡風險難以預測,但由于保險公司的客戶并不是單一個體,而是多個群體,所以投保人越多保險公司的損失風險就越分散,因此死亡率的變化并不會引起純保費的巨大變化。死亡率和利率是厘定壽險純保費的兩個主要因素,從歷史數(shù)據(jù)來看利率具有很強的隨機性,影響利率的因素很多,很難用一精確的數(shù)學方法來描繪利率的波動,傳統(tǒng)精算學中的利率從保單生效的那一刻起固定不變,壽險保單的有效期動輒幾十年,資金運作周期較長,利率的波動給保險公司帶來了巨大的風險。因此厘定保費時利率比死亡率更加重要,對隨機利率的研究符合社會發(fā)展的需求,越來越多的學者致力于隨機利率的研究。隨著當今社會人們生活成本的增加,分期付款應運而生。在購房或購車時,人們可以選擇按月繳費,但以往的壽險都是按年繳納保費。最近中國多家壽險公司相繼推出了新型壽險,這種新型壽險可以按季度繳費,甚至是按月繳費。因此,本文研究隨機利率下的分期繳費壽險精算模型。本文首先介紹隨機過程和壽險精算模型的一些基本概念。其次,采用Wiener過程與Poisson過程模擬利率的波動,構建了隨機利率下的分期繳費聯(lián)合壽險精算模型,分析了通貨膨脹對投保人的影響,將居民消費價格指數(shù)引入壽險精算模型中,構建了增額壽險精算模型。推導出了分期繳費形式下的躉繳純保費、均衡純保費、責任準備金以及保險公司損失風險。再次,分別在Gompertz假設和UDD假設條件下化簡了分期繳費壽險模型,得到了躉繳純保費、均衡純保費、責任準備金以及保險公司損失風險的相應表達式。最后,通過數(shù)值計算分析了給付函數(shù)、分期付款的次數(shù)以及投保期限等對保費與責任準備金的影響,并根據(jù)歷年的利率變化數(shù)據(jù)檢驗了隨機利率模型。該模型不僅能減少投保人繳納的保費,并且能夠減小保險公司損失風險,該模型具有實際應用價值。
[Abstract]:In real life, people may face the risk of death caused by disease and accidents. Although the risk of death faced by individuals is difficult to predict, the risk is stable from a group point of view. For an insurance company, the risk of death of a single policyholder is difficult to predict, but because the clients of the insurance company are not a single individual, but rather more groups, the more insured the insurance company, the more the risk of loss will be dispersed. So a change in mortality does not cause a huge change in net premiums. Mortality and interest rate are the two main factors in determining the net premium of life insurance. From the historical data, interest rate is very random, and there are many factors affecting interest rate. It is difficult to describe the fluctuation of interest rate by a precise mathematical method. The interest rate in traditional actuarial science is fixed from the moment when the policy becomes effective. The life insurance policy is valid for dozens of years and the capital operation period is longer. The fluctuation of interest rate brings huge risks to the insurance company. Therefore, the interest rate is more important than the death rate in determining the premium. The research on the stochastic interest rate meets the needs of social development. More and more scholars are devoted to the study of the stochastic interest rate. With the increase of people's living cost, installment payment arises at the historic moment. When buying a house or a car, people can choose to pay monthly, but in the past life insurance was paid annually. Recently, a number of Chinese life insurance companies have introduced new life insurance, this new life insurance can be paid quarterly, even monthly. Therefore, this paper studies the actuarial model of life insurance by installment under random interest rate. This paper first introduces some basic concepts of stochastic process and actuarial model of life insurance. Secondly, using the Wiener process and the Poisson process to simulate the fluctuation of interest rate, the combined life insurance actuarial model under the stochastic interest rate is constructed, and the influence of inflation on the policy holder is analyzed, and the consumer price index is introduced into the actuarial model of life insurance. The actuarial model of life insurance is constructed. The net premium, equilibrium premium, liability reserve and loss risk of insurance company are derived. Thirdly, under the Gompertz hypothesis and UDD hypothesis, we simplify the life insurance model by installment, and obtain the corresponding expressions of the net premium, equilibrium pure premium, liability reserve and the loss risk of insurance company. Finally, the effects of the payment function, the number of installments and the insured period on the premium and liability reserve are analyzed by numerical calculation, and the stochastic interest rate model is tested according to the interest rate variation data over the years. The model can not only reduce the insurance premium but also reduce the loss risk of the insurance company. The model has practical application value.
【學位授予單位】：哈爾濱工程大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F840.62;O211

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本文編號：1869270