本文選題：復(fù)合二項風(fēng)險模型 + 隨機(jī)收入�。� 參考：《湖南師范大學(xué)》2013年碩士論文

【摘要】：破產(chǎn)理論是近幾年來風(fēng)險理論研究的一個熱點課題.本文在經(jīng)典復(fù)合二項模型的基礎(chǔ)上,通過在保費(fèi)收入,索賠額分布等方面進(jìn)行推廣從而得到了不同離散的風(fēng)險模型,并重點研究了Gerber-Shui折罰函數(shù),期望折現(xiàn)分紅總量等破產(chǎn)特征量,主要做了下面幾個方面的工作： 1.基于具有隨機(jī)分紅的復(fù)合二項風(fēng)險模型,將保費(fèi)進(jìn)行推廣,不再是關(guān)于時間的一個線性函數(shù),而是一個二項過程.在該模型下,我們得到了折罰函數(shù)的遞推公式以及通過一個線性方程組來確定的Φ(0)(初始值為零時的Gerber-Shui折罰函數(shù)的值).最后,證明了線性方程組的解的唯一性以及給出了更新方程的解. 2.在隨機(jī)回報的復(fù)合二項風(fēng)險模型的基礎(chǔ)上,將該模型推廣為帶隨機(jī)回報的一類離散馬氏風(fēng)險模型,賠付的發(fā)生概率,賠付額的分布函數(shù)都有一個離散的馬氏鏈調(diào)控,當(dāng)保險公司采用門檻分紅策略時,通過計算得到了破產(chǎn)前的期望折現(xiàn)分紅總量滿足的一組線性方程組.最后,給出了期望折現(xiàn)分紅總量的顯示解析式. 3.在具有常紅利邊界和延遲索賠的一類更新離散的模型上,將保費(fèi)收入進(jìn)行推廣為一個二項過程,通過計算我們得到了帶新的邊界條件的期望折現(xiàn)分紅總量的微分方程組.最后,給出了期望分紅總量的顯示解析式.
[Abstract]:Bankruptcy theory is a hot topic in risk theory research in recent years. On the basis of the classical compound binomial model, the different discrete risk models are obtained by extending the premium income and the distribution of claim amount, and the Gerber-Shui penalty function is studied emphatically. Expected discounted dividends and other bankruptcy characteristics, mainly do the following aspects of work: 1. Based on the compound binomial risk model with stochastic dividend, the premium is generalized, which is no longer a linear function of time, but a binomial process. In this model, we obtain the recursive formula of the folding penalty function and the value of the Gerber-Shui penalty function determined by a linear equation set (the initial value is 00:00). Finally, the uniqueness of the solution of the linear system is proved and the solution of the renewal equation is given. 2. On the basis of the compound binomial risk model of random return, the model is extended to a discrete Markov risk model with random return. The probability of compensation and the distribution function of indemnity have a discrete Markov chain control. When the insurance company adopts the threshold dividend strategy, a set of linear equations for the total expected discounted dividend before bankruptcy is obtained by calculation. Finally, the display analytic formula of the total amount of expected discounted dividends is given. 3. On a class of updated discrete models with constant dividend boundary and delay claim, the premium income is generalized to a binomial process. By calculating the differential equations with new boundary conditions, we obtain the total expected discounted dividends. Finally, the display analytic formula of the total amount of expected dividends is given.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F842.3;O211.63

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