幾類廣義復合二項風險模型的破產問題研究
發(fā)布時間：2018-08-27 19:52
【摘要】：經典的二項風險模型是精算文獻中研究得最深入的離散時間更新風險過程,近些年來,許多精算學者從不同的方面把經典二項風險模型進行了推廣,得到了許多有價值的結論.在經典的復合二項風險模型的基礎上,本文研究幾類廣義復合二項風險模型,并且對這些模型的破產概率做了深入研究. 本論文共分為五章： 第一章本章首先對風險理論及其核心內容破產理論作簡要介紹,然后對經典復合二項風險模型做了綜合性的回顧,最后介紹了本文的主要工作. 第二章本章研究具有一般保費率的CCBM的破產概率,即索賠次數過程為一個復合二項過程,而保費率為一個非負整數.我們得到了該模型下最終破產概率的表達式和相應的上界估計. 第三章本章研究保費收入為復合二項過程的CCBM的破產概率,即假設保費收取次數服從復合二項分布,而索賠次數過程為一個復合復合二項過程,保費率為1,用鞅方法研究該模型下最終破產概率的表達式和相應的上界估計. 第四章本章研究保費收入為復合二項過程的帶擾動CCBM的破產概率,在前一章的基礎上考慮投資與干擾的因素,假設保費收取次數服從復合二項分布,而索賠次數過程為一個復合復合二項過程,建立一種貼近現實的新模型,得到最終破產概率的表達式和相應的上界估計. 第五章本章研究保費收入為復合二項過程的帶投資和擾動CCBM的破產概率,在上一章模型的基礎上考慮到投資利率和通貨膨脹等一些干擾因素對保險公司經營狀態(tài)影響,用鞅方法研究該模型下最終破產概率的表達式和相應的上界估計.
[Abstract]:The classical binomial risk model is the most deeply studied discrete time renewal risk process in the actuarial literature. In recent years, many actuarial scholars have extended the classical binomial risk model from different aspects and obtained many valuable conclusions. On the basis of classical compound binomial risk models, several generalized compound binomial risk models are studied in this paper, and the ruin probability of these models is studied deeply. This paper is divided into five chapters: the first chapter briefly introduces the risk theory and its core theory of bankruptcy, then makes a comprehensive review of the classical compound binomial risk model, and finally introduces the main work of this paper. In chapter 2, we study the ruin probability of CCBM with general premium rate, that is, the process of claim number is a compound binomial process, and the premium rate is a non-negative integer. We obtain the expression of the final ruin probability and the corresponding upper bound estimate. In Chapter 3, we study the ruin probability of CCBM, where the premium income is a compound binomial process, that is, assuming that the premium collection times are distributed from the compound binomial, and the claim number process is a compound binomial process. The premium rate is 1. The expression of the final ruin probability and the corresponding upper bound estimate are studied by martingale method. In chapter 4, we study the ruin probability of perturbed CCBM with a compound binomial process. On the basis of the previous chapter, we consider the factors of investment and disturbance, and assume that the premium collection times are distributed by compound binomial. The process of claim number is a compound binomial process. A new model close to reality is established, and the expression of the final ruin probability and the corresponding upper bound estimate are obtained. In chapter 5, we study the ruin probability with investment and perturbed CCBM when the premium income is a compound binomial process. On the basis of the model in the previous chapter, we consider the influence of some factors such as investment interest rate and inflation on the operating state of the insurance company. The expression of final ruin probability and the corresponding upper bound estimate are studied by martingale method.
【學位授予單位】：遼寧師范大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F840.4;F224
本文編號：2208289
[Abstract]:The classical binomial risk model is the most deeply studied discrete time renewal risk process in the actuarial literature. In recent years, many actuarial scholars have extended the classical binomial risk model from different aspects and obtained many valuable conclusions. On the basis of classical compound binomial risk models, several generalized compound binomial risk models are studied in this paper, and the ruin probability of these models is studied deeply. This paper is divided into five chapters: the first chapter briefly introduces the risk theory and its core theory of bankruptcy, then makes a comprehensive review of the classical compound binomial risk model, and finally introduces the main work of this paper. In chapter 2, we study the ruin probability of CCBM with general premium rate, that is, the process of claim number is a compound binomial process, and the premium rate is a non-negative integer. We obtain the expression of the final ruin probability and the corresponding upper bound estimate. In Chapter 3, we study the ruin probability of CCBM, where the premium income is a compound binomial process, that is, assuming that the premium collection times are distributed from the compound binomial, and the claim number process is a compound binomial process. The premium rate is 1. The expression of the final ruin probability and the corresponding upper bound estimate are studied by martingale method. In chapter 4, we study the ruin probability of perturbed CCBM with a compound binomial process. On the basis of the previous chapter, we consider the factors of investment and disturbance, and assume that the premium collection times are distributed by compound binomial. The process of claim number is a compound binomial process. A new model close to reality is established, and the expression of the final ruin probability and the corresponding upper bound estimate are obtained. In chapter 5, we study the ruin probability with investment and perturbed CCBM when the premium income is a compound binomial process. On the basis of the model in the previous chapter, we consider the influence of some factors such as investment interest rate and inflation on the operating state of the insurance company. The expression of final ruin probability and the corresponding upper bound estimate are studied by martingale method.
【學位授予單位】：遼寧師范大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F840.4;F224
【參考文獻】
相關期刊論文 前2條
1 龔日朝;鄒捷中;;復合二項風險模型下Gerber-Shiu折現懲罰函數的漸近解[J];系統(tǒng)科學與數學;2007年04期
2 彭丹;侯振挺;劉再明;;隨機利率下相依索賠的離散風險模型的分紅問題[J];應用數學學報;2011年06期
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