【摘要】：隨著世界金融體系的一體化和我國金融體系的進一步開放,我國的金融業特別是作為中國朝陽產業的保險業正面臨著前所未有的沖擊。破產風險是保險公司壓力測試的一個指標,提高破產風險的測量精度對于保險公司的風險控制、保費率厘定和準備金核算等精算問題的研究有非常重要的價值。 本文引入隨機模糊變量、交替更新過程和延遲交替更新過程,構建了基于交替與延遲交替更新過程的隨機模糊破產模型。論文的主要工作內容及取得的成果包括： 一、定義了隨機模糊環境下交替更新過程和延遲交替更新過程,并通過論證得到了幾個關于隨機模糊環境下的交替更新過程和延遲交替更新過程的重要定理,當交替更新變量和延遲交替更新變量服從隨機模糊指數分布時,研究了隨機模糊交替更新過程和隨機模糊延遲交替更新過程的分布函數、數學期望。 二、構建基于交替更新過程的隨機模糊破產模型時引入了隨機模糊變量、交替更新過程,當交替更新變量和索賠額變量是服從隨機模糊指數分布時,研究了索賠過程的期望、破產時刻的最終破產概率函數和最終破產機會均值。 三、構建基于延遲交替更新過程的隨機模糊破產模型時引入了隨機模糊變量、延遲交替更新過程,給出了延遲交替更新過程下的最終破產概率概率的一般結論,并且當延遲變量、交替更新變量和索賠額變量是服從隨機模糊指數分布時,研究了索賠過程的期望、破產時刻的最終破產概率函數和最終破產機會均值。 四、通過模型仿真和結果分析,揭示了模型的內涵意義和運算機制,將模型仿真結果與保險公司的現實情況進行了對比,進而驗證了所構建模型的科學性和實用性,并提出具有建設性的政策建議。 從模型的結構和仿真結果看出交替更新過程與延遲交替更新過程無論從現實意義還是從理論論證角度分析都符合保險公司的賠付過程,將二者定義在隨機模糊環境下去研究破產模型,使得模型更具有創新性和前瞻性。
[Abstract]:With the integration of the world financial system and the further opening of China's financial system, China's financial industry, especially the insurance industry as a sunrise industry, is facing an unprecedented impact. Bankruptcy risk is an index of stress testing for insurance companies. Improving the accuracy of bankruptcy risk measurement is of great value to the study of actuarial problems such as risk control, premium rate determination and reserve accounting of insurance companies. In this paper, a stochastic fuzzy ruin model based on alternating and delayed alternating renewal processes is constructed by introducing random fuzzy variables, alternating renewal processes and delayed alternating renewal processes. The main work and achievements are as follows: first, the alternating update process and the delayed alternating update process in random fuzzy environment are defined. Several important theorems about alternating renewal process and delayed alternating renewal process in random fuzzy environment are obtained. When alternating renewal variable and delayed alternating renewal variable are distributed by random fuzzy exponent, The distribution function and mathematical expectation of random fuzzy alternating renewal process and random fuzzy delay alternating renewal process are studied. Secondly, when constructing a stochastic fuzzy ruin model based on alternating renewal process, a stochastic fuzzy variable is introduced. The expectation of the claim process is studied when the alternating renewal variable and the claim amount variable are distributed according to the stochastic fuzzy exponential distribution. The final ruin probability function and the mean of the ultimate ruin opportunity at the ruin time. Thirdly, when constructing the stochastic fuzzy ruin model based on the delayed alternating renewal process, the random fuzzy variables and the delayed alternating renewal process are introduced, and the general conclusion of the final ruin probability under the delayed alternating renewal process is given. When the delay variable, alternate update variable and claim amount variable are distributed from random fuzzy exponent, the expectation of the claim process, the final ruin probability function at the ruin time and the mean value of the ultimate ruin opportunity are studied. Fourthly, through model simulation and result analysis, the connotation significance and operation mechanism of the model are revealed, and the results of model simulation are compared with the actual situation of insurance company, and the scientific and practical nature of the model is verified. And put forward constructive policy suggestions. From the structure of the model and the simulation results, it can be seen that the alternating renewal process and the delayed alternating renewal process are consistent with the insurance company's indemnity process both from the practical significance and from the theoretical point of view. The ruin model is studied by defining them in random fuzzy environment, which makes the model more innovative and forward-looking.
【學位授予單位】：華北電力大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F224;F840.3

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