重尾分布及其在風(fēng)險模型破產(chǎn)概率估計中的研究
發(fā)布時間：2018-12-13 23:00
【摘要】：破產(chǎn)理論是精算數(shù)學(xué)領(lǐng)域的一個重要部分,它不僅具有重要的理論研究價值,而且在金融保險公司風(fēng)險管理中有極強(qiáng)的實(shí)用價值。保險業(yè)作為金融業(yè)四大支柱之一,其本身也面臨索賠風(fēng)險,特別是對公司的經(jīng)營狀況有重大影響的“大額索賠”情形,此類索賠在數(shù)學(xué)上用重尾分布來刻畫。經(jīng)典的Lundberg-Cramer風(fēng)險模型是不考慮利息力因素的影響,但是在現(xiàn)實(shí)市場經(jīng)濟(jì)環(huán)境下利息力對投資者決策及其投資行為心理有重要影響,是保險公司必須要考慮的一個重要因素。 本論文的研究內(nèi)容是在重尾索賠下考慮利息力因素的離散時間風(fēng)險模型的破產(chǎn)概率。全文分為5章： 第1章是緒論,主要概述了破產(chǎn)理論的發(fā)展歷史,介紹了Lundberg-Cramer經(jīng)典風(fēng)險模型,并歸納了學(xué)者們推廣與改進(jìn)的風(fēng)險模型,最后總結(jié)了當(dāng)代破產(chǎn)理論幾個具有代表性的研究方向。 第2章是重尾分布及其子族,主要介紹了重尾分布的定義、重尾子族的劃分及重尾子族之間的相互關(guān)系。 第3章考慮了帶變利息力的離散時間風(fēng)險模型,將風(fēng)險模型通過盈余折現(xiàn)變形,假設(shè)個體凈風(fēng)險服從D∩L族和εRV族,分別得到有限時間和無限時間破產(chǎn)概率的一致尾等價關(guān)系式及其上下界表達(dá)式。 第4章考慮的是帶Markov鏈利息力的離散時間風(fēng)險模型,在個體凈風(fēng)險服從R-α族和相關(guān)重尾假設(shè)下,利用全概率公式和遞推方法,得到有限時間離散風(fēng)險模型破產(chǎn)概率的近似表達(dá)式。 第5章對全文的研究結(jié)果做了總結(jié),并介紹了作者下一步的工作計劃。
[Abstract]:Bankruptcy theory is an important part in the field of actuarial mathematics. It not only has important theoretical research value, but also has a strong practical value in risk management of financial insurance companies. As one of the four pillars of the financial industry, the insurance industry itself also faces the risk of claim, especially the "large claim" situation, which has a significant impact on the company's operating conditions. This kind of claim is mathematically characterized by heavy-tailed distribution. The classical Lundberg-Cramer risk model does not consider the influence of interest force, but in the real market economy, interest force has an important influence on investors' decision-making and investment behavior psychology, which is an important factor that insurance companies must consider. In this paper, the ruin probability of discrete-time risk model with interest force is considered in heavy-tailed claims. The thesis is divided into five chapters: the first chapter is the introduction, which summarizes the development history of bankruptcy theory, introduces the classical risk model of Lundberg-Cramer, and summarizes the risk model which is popularized and improved by scholars. Finally, several representative research directions of contemporary bankruptcy theory are summarized. In chapter 2, we introduce the definition of heavy-tailed distribution, the division of heavy-tailed sub-family and the relationship between heavy-tailed subfamilies. In chapter 3, the discrete time risk model with variable interest force is considered, and the risk model is deformed by surplus. The uniform tail equivalent relation and its upper and lower bound expressions of the ruin probability of finite time and infinite time are obtained respectively. In chapter 4, the discrete time risk model with interest force of Markov chain is considered. Under the assumption of R- 偽 family and related heavy tail, the full probability formula and recursive method are used. The approximate expression of ruin probability of finite time discrete risk model is obtained. Chapter 5 summarizes the research results and introduces the author's next work plan.
【學(xué)位授予單位】：安徽工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F840.3;O211.3
本文編號：2377405
[Abstract]:Bankruptcy theory is an important part in the field of actuarial mathematics. It not only has important theoretical research value, but also has a strong practical value in risk management of financial insurance companies. As one of the four pillars of the financial industry, the insurance industry itself also faces the risk of claim, especially the "large claim" situation, which has a significant impact on the company's operating conditions. This kind of claim is mathematically characterized by heavy-tailed distribution. The classical Lundberg-Cramer risk model does not consider the influence of interest force, but in the real market economy, interest force has an important influence on investors' decision-making and investment behavior psychology, which is an important factor that insurance companies must consider. In this paper, the ruin probability of discrete-time risk model with interest force is considered in heavy-tailed claims. The thesis is divided into five chapters: the first chapter is the introduction, which summarizes the development history of bankruptcy theory, introduces the classical risk model of Lundberg-Cramer, and summarizes the risk model which is popularized and improved by scholars. Finally, several representative research directions of contemporary bankruptcy theory are summarized. In chapter 2, we introduce the definition of heavy-tailed distribution, the division of heavy-tailed sub-family and the relationship between heavy-tailed subfamilies. In chapter 3, the discrete time risk model with variable interest force is considered, and the risk model is deformed by surplus. The uniform tail equivalent relation and its upper and lower bound expressions of the ruin probability of finite time and infinite time are obtained respectively. In chapter 4, the discrete time risk model with interest force of Markov chain is considered. Under the assumption of R- 偽 family and related heavy tail, the full probability formula and recursive method are used. The approximate expression of ruin probability of finite time discrete risk model is obtained. Chapter 5 summarizes the research results and introduces the author's next work plan.
【學(xué)位授予單位】：安徽工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F840.3;O211.3
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相關(guān)期刊論文 前5條
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