本文選題：破產(chǎn)時刻　切入點：破產(chǎn)概率　出處：《蘭州交通大學(xué)》2012年碩士論文

【摘要】：本文研究了幾類風(fēng)險模型以及風(fēng)險模型的改進模型的破產(chǎn)上界。主要運用了鞅方法和遞歸方法兩種求解風(fēng)險模型破產(chǎn)上界的方法對幾類風(fēng)險模型以及風(fēng)險模型的改進模型進行預(yù)測和比較,從而得到哪種方法得到的結(jié)果擬合度更高,并且研究了公司破產(chǎn)中的相關(guān)變量對破產(chǎn)概率以及破產(chǎn)上界的影響。最終通過實例分析得到了降低公司破產(chǎn)風(fēng)險的方法。 本文共包括四章： 第一章,概述了經(jīng)典風(fēng)險模型的背景知識以及在近百年間得到的一些有關(guān)精算方面的經(jīng)典理論,已經(jīng)取得的研究成果,介紹了兩種得到最終破產(chǎn)上界的方法,同時簡要介紹了本文的選題意義和內(nèi)容。 第二章,介紹了廣義復(fù)合Poisson風(fēng)險模型以及帶擴展擾動項的復(fù)合Poisson模型,并給出了相應(yīng)的破產(chǎn)概率的理論證明,并最終得到帶干擾的非齊次Poisson風(fēng)險模型破產(chǎn)概率上界,雙復(fù)合Poisson風(fēng)險模型破產(chǎn)概率上界,在實例分析中分別運用了兩種求解方法求解破產(chǎn)上界并對結(jié)果進行比較。最后通過數(shù)值模擬比較出了它們的優(yōu)劣性。 第三章,總結(jié)和歸納了含有正、負(fù)風(fēng)險和的模型和只含有負(fù)風(fēng)險和的組合模型。從模型的構(gòu)建著手,對兩類模型進行對比并分別列出他們的數(shù)字特征。最終分別求解兩類模型的破產(chǎn)概率的破產(chǎn)上界。 第四章,從前幾章對破產(chǎn)概率以及破產(chǎn)上界求解的基礎(chǔ)上對兩類Erlang(2)更新風(fēng)險模型的破產(chǎn)概率以及破產(chǎn)上界進行分析和研究,首先介紹兩類更新Erlang(2)風(fēng)險模型,然后通過對傳統(tǒng)風(fēng)險模型的破產(chǎn)概率的研究方法對兩類更新風(fēng)險模型的破產(chǎn)概率進行求解,后又引出了Erlang(n)的一般性破產(chǎn)概率問題,并證明求解了Erlang(n)下和廣義Erlang(n)下的罰金函數(shù)和破產(chǎn)概率。最終得到了Erlang(2)下的破產(chǎn)上界。文章最后進行了實例分析,并得出結(jié)論：防范利率風(fēng)險,密切關(guān)注國家經(jīng)濟走勢和銀行政策是降低保險公司經(jīng)營風(fēng)險的有效保障；合理的公司并購是分散保險公司經(jīng)營風(fēng)險的有效途徑。在幾類方法求解保險公司破產(chǎn)上界的對比中遞歸方法明顯優(yōu)于鞅方法,鞅方法和遞歸方法較Lundberg上界又都有所改進和優(yōu)化。
[Abstract]:In this paper, we study the ruin upper bounds of several kinds of risk models and their improved models. We mainly use martingale method and recursive method to solve the ruin upper bounds of risk models. Improved models for prediction and comparison, Finally, the method of reducing the risk of corporate bankruptcy is obtained by analyzing the influence of the relative variables on the ruin probability and the upper bound of bankruptcy. This paper consists of four chapters:. In the first chapter, the background knowledge of the classical risk model and some classical actuarial theories obtained in the past 100 years are summarized, and two methods to obtain the ultimate upper bound of bankruptcy are introduced. At the same time, it briefly introduces the significance and content of this paper. In chapter 2, the generalized compound Poisson risk model and the compound Poisson model with extended perturbed term are introduced, and the corresponding ruin probability theory proof is given. Finally, the upper bound of ruin probability of nonhomogeneous Poisson risk model with disturbance is obtained. The ruin probability upper bound of double compound Poisson risk model is solved by two methods in case analysis and the results are compared. Finally, the advantages and disadvantages of these two methods are compared by numerical simulation. In the third chapter, we summarize and summarize the model with positive and negative risk sum and the combination model with only negative risk sum. The two kinds of models are compared and their numerical characteristics are listed respectively. Finally, the ruin upper bound of the ruin probability of the two kinds of models is solved respectively. In chapter 4, we analyze and study the ruin probability and ruin upper bound of two kinds of Erlang2) renewal risk models based on the ruin probability and the solution of the upper bound of bankruptcy in the previous chapters. Firstly, we introduce two kinds of updated Erlang2) risk models. Then the ruin probability of two kinds of renewal risk models is solved by the method of studying the ruin probability of traditional risk model, and then the general ruin probability problem of Erlangn is introduced. It is proved that the penalty function and ruin probability under Erlangn) and generalized Erlangn) are solved. Finally, the upper bound of bankruptcy under Erlangn 2) is obtained. Paying close attention to the trend of national economy and bank policy is an effective guarantee to reduce the risk of insurance company management. Reasonable M & A is an effective way to disperse the business risk of insurance companies. The recursive method is obviously superior to the martingale method in the comparison of several methods to solve the upper bound of bankruptcy of the insurance company, and the martingale method and recursive method are both improved and optimized compared with the Lundberg upper bound.
【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F224;F840

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