【摘要】：本文主要研究的是重尾索賠風險模型的破產(chǎn)概率及相應的數(shù)值模擬.在金融保險業(yè)中,對巨災產(chǎn)生的大額索賠事件的研究一直是一個熱點,這些極端事件不經(jīng)常發(fā)生,一旦發(fā)生,將會給保險業(yè)務帶來重大風險,可能會讓保險公司陷入財務危機,甚至破產(chǎn).近年來,眾多學者已經(jīng)對這些現(xiàn)象進行了大量研究,其中對保險公司破產(chǎn)概率漸近估計的研究更是備受青睞.在眾多專家學者的努力下,得到了滿足各種不同條件的漸近表達式,但這些研究成果大部分是理論結果,缺乏實踐意義.近幾年,眾多國內外學者已經(jīng)不滿足將研究停留在理論結果上,而是趨向于驗證理論結果是否合理,并取得了不錯的進展.本文在已有研究成果的基礎上有了理論突破,更進一步做了matlab模擬,驗證了理論知識的合理性. 此外,本文在考慮重尾現(xiàn)象的同時,還考慮風險索賠之間的相依性.近幾年,對保險風險理論的研究多集中在相依情況下.本文也將理論結果擴展到了相依的情況,即上尾相依的特殊情形 上尾獨立,使之更貼近實際. 本文主要由三部分組成. 第一章主要介紹了經(jīng)典風險模型及其推廣形式,畫出了各種情況下盈余過程的樣本軌道圖,并進行了比較. 第二章主要內容為潛在索賠風險模型在重尾分布條件下的破產(chǎn)概率和數(shù)值模擬.在潛在索賠額序列服從S族的假設下,得到了有限時間破產(chǎn)概率的漸近表達式,并給出了模擬結果. 第三章是對上尾獨立情形下潛在索賠風險模型有限時間破產(chǎn)概率的研究,假設索賠額序列是上尾獨立同分布的重尾隨機變量序列,潛在索賠額序列服從L∩D族,得到了有限時間破產(chǎn)概率的漸近表達式.
[Abstract]:In this paper, the ruin probability of heavy tail claim risk model and its corresponding numerical simulation are studied. In the financial and insurance industry, the study of large claims caused by catastrophe has always been a hot spot. These extreme events do not occur frequently. Once they occur, they will bring significant risks to the insurance business and may lead to financial crisis for insurance companies. Even bankruptcy. In recent years, many scholars have done a lot of research on these phenomena, among which, the research on the asymptotic estimation of bankruptcy probability of insurance companies is more and more popular. Through the efforts of many experts and scholars, the asymptotic expressions satisfying various conditions are obtained, but most of these research results are theoretical results and lack of practical significance. In recent years, many scholars at home and abroad have not satisfied to stay on the theoretical results, but tend to verify whether the theoretical results are reasonable, and have made good progress. In this paper, based on the existing research results, a theoretical breakthrough has been made, and further matlab simulation has been done to verify the rationality of the theoretical knowledge. In addition, we consider the dependence of risk claims as well as the heavy-tailed phenomenon. In recent years, the study of insurance risk theory is mostly focused on dependent cases. In this paper, the theoretical results are extended to the dependent case, that is, the special case of the dependency of the upper tail and the tail is independent, so that it is closer to the reality. This paper mainly consists of three parts. The first chapter mainly introduces the classical risk model and its extension form, draws the sample track diagram of the surplus process under various circumstances, and compares it with each other. The second chapter focuses on the ruin probability and numerical simulation of the potential claim risk model under the condition of heavy-tailed distribution. Under the assumption of S family, the asymptotic expression of ruin probability in finite time is obtained, and the simulation results are given. In the third chapter, we study the finite time ruin probability of the potential claim risk model in the case of upper tail independence, assuming that the claim amount sequence is a sequence of heavy-tailed random variables with the same distribution of upper tail independence, and the potential claim amount sequence is followed by L 鈮，

本文編號：2230369