本文選題：風(fēng)險(xiǎn)模型 + 破產(chǎn)概率�。� 參考：《哈爾濱理工大學(xué)》2012年碩士論文

【摘要】：風(fēng)險(xiǎn)理論主要研究保險(xiǎn)行業(yè)中的隨機(jī)風(fēng)險(xiǎn)模型，它是金融學(xué)和精算學(xué)的基礎(chǔ)理論，也是精算界研究的熱門(mén)問(wèn)題之一．作為風(fēng)險(xiǎn)理論的核心問(wèn)題，破產(chǎn)理論是大多數(shù)學(xué)者們熱衷討論的課題．而破產(chǎn)理論中破產(chǎn)概率在風(fēng)險(xiǎn)理論中具有重要應(yīng)用．一方面，破產(chǎn)概率可以為保險(xiǎn)公司運(yùn)營(yíng)情況和保險(xiǎn)公司的領(lǐng)導(dǎo)者提供一個(gè)危險(xiǎn)提示；另一方面，它是判斷保險(xiǎn)公司中某一個(gè)險(xiǎn)種能否承受金融風(fēng)險(xiǎn)的重要理論依據(jù)；更重要的是，它保證了保險(xiǎn)公司的正常運(yùn)營(yíng)，，對(duì)保險(xiǎn)監(jiān)督部門(mén)的監(jiān)管提供有力依據(jù)．正是由于破產(chǎn)概率在風(fēng)險(xiǎn)理論中的重要應(yīng)用，對(duì)破產(chǎn)概率的研究具有重要的理論意義和實(shí)際價(jià)值．鞅論作為研究風(fēng)險(xiǎn)理論的首要方法，正逐漸成為一個(gè)非常重要的數(shù)學(xué)工具應(yīng)用到各個(gè)領(lǐng)域中，特別是在保險(xiǎn)行業(yè)中的應(yīng)用． 本文在帶支出因素下的負(fù)二項(xiàng)風(fēng)險(xiǎn)模型的理論研究基礎(chǔ)上，結(jié)合以往學(xué)者的研究結(jié)果，對(duì)經(jīng)典風(fēng)險(xiǎn)模型進(jìn)行了詳盡的說(shuō)明，并且考慮了通貨膨脹率以及支出兩方面的因素，建立新的雙poisson風(fēng)險(xiǎn)模型． 本文研究?jī)?nèi)容及結(jié)果主要體現(xiàn)在以下幾個(gè)方面： 1.首先給出本文所涉及到的鞅方法與停時(shí)定理的相關(guān)理論，介紹了經(jīng)典風(fēng)險(xiǎn)模型及其推廣． 2.在已有的廣義雙poisson風(fēng)險(xiǎn)模型的基礎(chǔ)上，考慮了通貨膨脹率及支出兩方面的因素，將保費(fèi)的收入過(guò)程、理賠過(guò)程都考慮成poisson過(guò)程，支出過(guò)程考慮為維納過(guò)程，從而建立新的模型．在此基礎(chǔ)上，運(yùn)用鞅方法得出模型的最終破產(chǎn)概率． 3.在通貨膨脹率及支出兩方面的因素下，考慮到保險(xiǎn)行業(yè)的現(xiàn)實(shí)情況，將單險(xiǎn)種擴(kuò)展到雙險(xiǎn)種的情況，進(jìn)而建立新的模型．同樣運(yùn)用鞅方法，得到模型的破產(chǎn)概率及Lundberg表達(dá)式．
[Abstract]:The risk theory mainly studies the stochastic risk model in the insurance industry, which is the basic theory of finance and actuarial science, and also one of the hot problems in the actuarial field. Bankruptcy theory is a topic that most scholars are keen to discuss. But bankruptcy probability has important application in risk theory. On the one hand, The probability of bankruptcy can provide a dangerous hint for the operation of the insurance company and the leader of the insurance company; on the other hand, it is an important theoretical basis for judging whether an insurance company can withstand financial risks; more importantly, It ensures the normal operation of the insurance company and provides a strong basis for the supervision of the insurance supervision department. It is precisely because of the important application of bankruptcy probability in the risk theory, The study of ruin probability has important theoretical significance and practical value. Martingale theory, as the first method of studying risk theory, is gradually becoming a very important mathematical tool to be applied in every field. Especially in the insurance industry. On the basis of the theoretical study of negative binomial risk model with expenditure factors and combined with the research results of previous scholars, this paper gives a detailed explanation of the classical risk model. Considering two factors of inflation and expenditure, a new double poisson risk model is established. The main contents and results of this paper are as follows: 1. Firstly, the theory of martingale method and stopping time theorem is given, and the classical risk model and its generalization are introduced. 2. On the basis of the generalized double poisson risk model, inflation rate and expenditure are taken into account. The process of premium income and claim is considered as poisson process, and the process of expenditure is considered as Wiener process. On the basis of this, the final ruin probability of the model is obtained by using martingale method. Under the two factors of inflation rate and expenditure, considering the actual situation of insurance industry, the single insurance type is extended to the double insurance type case, and a new model is established. The ruin probability and Lundberg expression of the model are also obtained by using martingale method.
【學(xué)位授予單位】：哈爾濱理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類(lèi)號(hào)】：F224;F840;F820.5

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