本文選題：風(fēng)險模型　切入點：破產(chǎn)概率　出處：《燕山大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：本文是在經(jīng)典的復(fù)合Poisson風(fēng)險模型的基礎(chǔ)上，，對再保險風(fēng)險模型進(jìn)行研究，主要研究比例再保險和超額賠款再保險。根據(jù)實際需要，對復(fù)合Poisson過程進(jìn)行推廣，討論保費收取次數(shù)為負(fù)二項隨機過程，索賠次數(shù)為Poisson-Geometric過程的風(fēng)險模型。 首先介紹了相關(guān)的理論知識，對風(fēng)險模型，破產(chǎn)概率，調(diào)節(jié)系數(shù)，鞅方法，負(fù)二項分布，Poisson-Geometric分布和Cox過程的相關(guān)理論進(jìn)行了介紹。 其次研究多險種的復(fù)合Poisson過程的再保險風(fēng)險模型。首先研究復(fù)合Poisson過程的比例再保險風(fēng)險模型，考慮了帶有利率，通貨膨脹率和破產(chǎn)下限的風(fēng)險模型，得出了破產(chǎn)概率的表達(dá)式，當(dāng)再保險比例系數(shù)越大時，調(diào)節(jié)系數(shù)越大，破產(chǎn)概率越��；然后研究復(fù)合Poisson過程的超額賠款再保險風(fēng)險模型，得到了調(diào)節(jié)系數(shù)的上下界；最后考慮了帶Cox過程的多險種風(fēng)險模型，得出了破產(chǎn)概率的表達(dá)式，當(dāng)原保險公司賠款上限越大時，調(diào)節(jié)系數(shù)越小，破產(chǎn)概率越大。 接下來研究保費到達(dá)過程為負(fù)二項隨機過程的再保險風(fēng)險模型。首先研究負(fù)二項隨機過程的比例再保險風(fēng)險模型，得出了破產(chǎn)概率的表達(dá)式；其次考慮出現(xiàn)主索賠及延遲索賠時的風(fēng)險模型，也得到了此模型的破產(chǎn)概率；最后研究負(fù)二項隨機過程的超額賠款再保險風(fēng)險模型，考慮了帶有隨機擾動項的風(fēng)險模型，得出了當(dāng)索賠為指數(shù)分布時，調(diào)節(jié)系數(shù)與超額賠款上限M的關(guān)系。 最后研究復(fù)合Poisson-Geometric過程再保險的風(fēng)險模型。首先研究復(fù)合Poisson-Geometric過程的比例再保險風(fēng)險模型，考慮了退保事件，其中保費總額服從復(fù)合負(fù)二項隨機過程，理賠總額服從復(fù)合Poisson-Geometric過程，退�？傤~服從復(fù)合二項隨機過程，給出破產(chǎn)概率的表達(dá)式；其次研究復(fù)合Poisson-Geometric過程的超額賠款再保險風(fēng)險模型，考慮了調(diào)節(jié)系數(shù)與超額賠款上限M的關(guān)系。
[Abstract]:In this paper, based on the classical composite Poisson risk model, the risk model of reinsurance is studied, the proportional reinsurance and excess reinsurance are studied. According to the actual needs, the composite Poisson process is generalized. This paper discusses a risk model in which the number of premium collection is negative binomial stochastic process and the number of claims is Poisson-Geometric process. Firstly, the relevant theories are introduced, such as risk model, ruin probability, adjustment coefficient, martingale method, negative binomial distribution Poisson-Geometric distribution and Cox process. Secondly, the reinsurance risk model of compound Poisson process with multiple types of insurance is studied. Firstly, the proportional reinsurance risk model of compound Poisson process is studied, and the risk model with interest rate, inflation rate and bankruptcy floor is considered. The expression of ruin probability is obtained, when the ratio coefficient of reinsurance is larger, the adjustment coefficient is larger, and the ruin probability is smaller. Then, the risk model of excess indemnity reinsurance in compound Poisson process is studied, and the upper and lower bounds of adjustment coefficient are obtained. Finally, the multi-insurance risk model with Cox process is considered, and the expression of ruin probability is obtained. When the upper limit of indemnity of the original insurance company is higher, the adjustment coefficient is smaller and the ruin probability is higher. Then we study the reinsurance risk model in which the premium arrival process is a negative binomial stochastic process. Firstly, the proportional reinsurance risk model of the negative binomial stochastic process is studied, and the expression of ruin probability is obtained. Secondly, considering the risk model of the main claim and the delay claim, the ruin probability of the model is also obtained. Finally, the risk model of excess indemnity reinsurance for the negative binomial stochastic process is studied, and the risk model with random disturbance is considered. When the claim is exponentially distributed, the relationship between the adjustment coefficient and the upper limit M of excess compensation is obtained. Finally, the risk model of reinsurance in compound Poisson-Geometric process is studied. Firstly, the proportional reinsurance risk model of compound Poisson-Geometric process is studied, and the event of reinsurance is considered, in which the total premium is from the compound negative binomial stochastic process, and the total claim is from the compound Poisson-Geometric process. The expression of ruin probability is given from the compound binomial stochastic process. Secondly, the risk model of excess indemnity reinsurance in compound Poisson-Geometric process is studied, and the relationship between the adjustment coefficient and the upper limit M of excess indemnity is considered.
【學(xué)位授予單位】：燕山大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F840.3;F224

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