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The Research of Compound Negative Binomial Risk Model

Author: ZhangXinLiang
Tutor: WangZhiMing
School: Wuhan University of Science and Technology
Course: Probability Theory and Mathematical Statistics
Keywords: Negative binomial distribution Probability of ruin Minimum Dynamic bankruptcy with Surplus process
CLC: F840
Type: Master's thesis
Year: 2009
Downloads: 12
Quote: 0
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Abstract


Risk model , bankruptcy probability problems through modeling and prediction , from a quantitative point of view on the insurance company is in different stages of risk given measure , the establishment of a comprehensive risk prediction mechanism , in order to formulate a more reasonable insurance strategy to reduce market risk . face the new problems of today 's field of insurance and insurance of the growing diversity and complexity , insurance companies need and so the development of a more diversified and practical financial products . This paper studies the number of claims to obey negative item distribution of the case , combined with the actual situation in today 's insurance practice , at different stages may define different minimum bankruptcy limit of ruin that dynamic . as of risk Model based distribution as a research base for various process . Firstly, starting from a variety of distribution types , introduced a variety of distribution , and combined in the insurance business loss claims refine the definition and analysis , to study the nature and laws of the compound distribution . important example of the mixture distribution in the insurance business for the final the model to provide a theoretical basis in the fourth chapter of the next , using the previously established theoretical basis , the surplus process specifically discussed the definition of negative binomial random distribution of the number of claims . analysis of the nature of the ruin probability and the adjustment coefficient adjustment coefficient estimates and the establishment of the bankruptcy probability prediction equation . while taking advantage of the utility function of the premium to develop insurance policy . , the introduction of dynamic minimum ruin probability in the last the surplus process integration follow a negative binomial distribution of the number of claims , prove the presence of the adjustment coefficient , deduced Lundberg inequality , and to explore the compound Poisson distribution with composite surplus process can be converted to the negative binomial distribution .

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CLC: > Economic > Fiscal, monetary > Insurance > Insurance Theory
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