發(fā)布時(shí)間：2018-05-10 12:16

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

【摘要】：在實(shí)際生活中,人們可能會(huì)面臨疾病和意外事故所帶來的死亡風(fēng)險(xiǎn),雖然個(gè)體面臨的死亡風(fēng)險(xiǎn)難以預(yù)測,但從群體角度來看,風(fēng)險(xiǎn)具有穩(wěn)定性。對(duì)保險(xiǎn)公司來說,單個(gè)投保人的死亡風(fēng)險(xiǎn)難以預(yù)測,但由于保險(xiǎn)公司的客戶并不是單一個(gè)體,而是多個(gè)群體,所以投保人越多保險(xiǎn)公司的損失風(fēng)險(xiǎn)就越分散,因此死亡率的變化并不會(huì)引起純保費(fèi)的巨大變化。死亡率和利率是厘定壽險(xiǎn)純保費(fèi)的兩個(gè)主要因素,從歷史數(shù)據(jù)來看利率具有很強(qiáng)的隨機(jī)性,影響利率的因素很多,很難用一精確的數(shù)學(xué)方法來描繪利率的波動(dòng),傳統(tǒng)精算學(xué)中的利率從保單生效的那一刻起固定不變,壽險(xiǎn)保單的有效期動(dòng)輒幾十年,資金運(yùn)作周期較長,利率的波動(dòng)給保險(xiǎn)公司帶來了巨大的風(fēng)險(xiǎn)。因此厘定保費(fèi)時(shí)利率比死亡率更加重要,對(duì)隨機(jī)利率的研究符合社會(huì)發(fā)展的需求,越來越多的學(xué)者致力于隨機(jī)利率的研究。隨著當(dāng)今社會(huì)人們生活成本的增加,分期付款應(yīng)運(yùn)而生。在購房或購車時(shí),人們可以選擇按月繳費(fèi),但以往的壽險(xiǎn)都是按年繳納保費(fèi)。最近中國多家壽險(xiǎn)公司相繼推出了新型壽險(xiǎn),這種新型壽險(xiǎn)可以按季度繳費(fèi),甚至是按月繳費(fèi)。因此,本文研究隨機(jī)利率下的分期繳費(fèi)壽險(xiǎn)精算模型。本文首先介紹隨機(jī)過程和壽險(xiǎn)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(dòng),構(gòu)建了隨機(jī)利率下的分期繳費(fèi)聯(lián)合壽險(xiǎn)精算模型,分析了通貨膨脹對(duì)投保人的影響,將居民消費(fèi)價(jià)格指數(shù)引入壽險(xiǎn)精算模型中,構(gòu)建了增額壽險(xiǎn)精算模型。推導(dǎo)出了分期繳費(fèi)形式下的躉繳純保費(fèi)、均衡純保費(fèi)、責(zé)任準(zhǔn)備金以及保險(xiǎn)公司損失風(fēng)險(xiǎn)。再次,分別在Gompertz假設(shè)和UDD假設(shè)條件下化簡了分期繳費(fèi)壽險(xiǎn)模型,得到了躉繳純保費(fèi)、均衡純保費(fèi)、責(zé)任準(zhǔn)備金以及保險(xiǎn)公司損失風(fēng)險(xiǎn)的相應(yīng)表達(dá)式。最后,通過數(shù)值計(jì)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(duì)保費(fèi)與責(zé)任準(zhǔn)備金的影響,并根據(jù)歷年的利率變化數(shù)據(jù)檢驗(yàn)了隨機(jī)利率模型。該模型不僅能減少投保人繳納的保費(fèi),并且能夠減小保險(xiǎn)公司損失風(fēng)險(xiǎn),該模型具有實(shí)際應(yīng)用價(jià)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(xué)位授予單位】：哈爾濱工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F840.62;O211

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本文編號(hào)：1869270