發(fā)布時間：2018-05-23 17:12

  本文選題：重尾分布 + 破產(chǎn)概率　； 參考：《華東師范大學(xué)》2014年博士論文

【摘要】：在保險精算中,有些極端事件,比如洪災(zāi)、地震、火山噴發(fā)等,一旦發(fā)生就會對保險公司產(chǎn)生嚴重的沖擊,造成保險公司運營困難,有的甚至導(dǎo)致其破產(chǎn).而且近年來這類事件也頻繁發(fā)生.因此人們越來越重視對重尾理賠額所驅(qū)動的風(fēng)險過程的研究.鑒于此,本文考慮了幾類重尾風(fēng)險模型.具體內(nèi)容如下： 1.第一章首先闡述了本文的研究背景.接著,介紹了常見的重尾分布族.然后,介紹了標準更新風(fēng)險模型及破產(chǎn)概率的定義.最后,給出了一些基本概念和定理及本論文的主要工作. 2.第二章研究了帶投資的二維風(fēng)險模型的破產(chǎn)概率.考慮同一家保險公司的兩種不同險種的索賠同時到達的情況.在二維框架下研究了兩種類型的破產(chǎn).利用鞅方法得到了最終破產(chǎn)概率的上界.對于這兩種類型的破產(chǎn)分別得到了生存概率滿足的積分-微分方程,以及有限時間破產(chǎn)概率的漸近表達式. 3.第三章考慮了帶常利率的二維風(fēng)險模型的破產(chǎn)概率.在本章的模型中,每一次索賠是由兩家保險公司按一定的比例來支付.在二維框架下研究了兩種類型的破產(chǎn),對于這兩種類型的破產(chǎn)分別得到了生存概率滿足的積分-微分方程,以及有限時間破產(chǎn)概率的漸近表達式. 4.第四章研究了帶常利率的復(fù)合泊松風(fēng)險模型的Gerber-Shiu罰金函數(shù)和破產(chǎn)概率.得到了罰金函數(shù)滿足的積分-微分方程.從而得到了破產(chǎn)概率滿足的積分-微分方程.由此出發(fā)還得到了破產(chǎn)概率的漸近表達式. 5.第五章考慮了隨機保費收入風(fēng)險模型破產(chǎn)概率的一致漸近性.得到了有限時破產(chǎn)概率和最終破產(chǎn)概率的漸近表達式,并且獲得的漸近表達式對時間一致成立. 6.第六章研究了帶隨機利率的離散時間風(fēng)險模型的破產(chǎn)概率.在索賠額的分布屬于D∩L族的條件下,得到了最終破產(chǎn)概率的漸近表達式.
[Abstract]:In actuarial insurance, some extreme events, such as floods, earthquakes, volcanic eruptions and so on, will have a serious impact on insurance companies once they occur, resulting in the operation of insurance companies difficult, some even lead to bankruptcy. And in recent years, such incidents have occurred frequently. Therefore, people pay more and more attention to the risk process driven by heavy-tailed claims. In view of this, several kinds of heavy tail risk models are considered in this paper. The details are as follows: 1. The first chapter describes the background of this paper. Then, the common heavy-tailed distribution family is introduced. Then, the standard renewal risk model and the definition of ruin probability are introduced. Finally, some basic concepts and theorems are given, as well as the main work of this paper. 2. In chapter 2, the ruin probability of two-dimensional risk model with investment is studied. Consider the simultaneous arrival of claims for two different types of insurance from the same insurance company. Two types of bankruptcy are studied in a two-dimensional framework. The upper bound of the final ruin probability is obtained by using martingale method. For these two types of ruin, the asymptotic expressions of the integro-differential equation satisfying the survival probability and the ruin probability of finite time are obtained respectively. 3. In chapter 3, the ruin probability of two-dimensional risk model with constant interest rate is considered. In the model of this chapter, each claim is paid by two insurance companies in proportion. In this paper, two types of ruin are studied in a two-dimensional framework. For these two types of ruin, the integro-differential equations satisfying the survival probability and the asymptotic expression of the ruin probability in finite time are obtained, respectively. 4. In chapter 4, the Gerber-Shiu penalty function and ruin probability of compound Poisson risk model with constant interest rate are studied. The integro-differential equation satisfying the fine function is obtained. Thus, the integro-differential equation satisfying the ruin probability is obtained. The asymptotic expression of ruin probability is also obtained. 5. In chapter 5, we consider the uniform asymptotic property of ruin probability of stochastic premium income risk model. The asymptotic expressions of finite ruin probability and final ruin probability are obtained, and the obtained asymptotic expressions are consistent with time. 6. In chapter 6, the ruin probability of discrete time risk model with stochastic interest rate is studied. The asymptotic expression of the final ruin probability is obtained under the condition that the distribution of the claim amount belongs to the D class of L.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：F224;F840

【參考文獻】

相關(guān)期刊論文 前1條

1 ;FINITE-TIME RUIN PROBABILITY WITH NQD DOMINATED VARYING-TAILED CLAIMS AND NLOD INTER-ARRIVAL TIMES[J];Journal of Systems Science & Complexity;2009年03期

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本文編號：1925629