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A Study on Mathematical Risk Model of Insurance

Author: BaiXiaoMing
Tutor: LiPing
School: Huazhong University of Science and Technology
Course: Probability and Mathematical Statistics
Keywords: Insurance Risk model Probability of ruin Martingale Lundberg inequality
CLC: F224
Type: Master's thesis
Year: 2005
Downloads: 309
Quote: 1
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Abstract

Risk theory is to take advantage of the knowledge and methods of probability theory and stochastic processes, based on the practical problems of insurance companies operating in the establishment of the mathematical model, the surplus of the insurance study, given the method of calculation of the premiums and ruin probability, adjustment coefficient other aspects of the analysis, the solvency of insurance companies practice the key concern of the insurer, the ruin probability that the size of the operators of the possibility of bankruptcy, given the stability of operations and the inability to repay a certain measure portrayed bankruptcy probability The problem has been the risk theory, especially the bankruptcy important topic of theoretical research. Text from many perspectives on the basis of classical risk model improved risk model under different scenarios, given the corresponding model under the satisfied expression of ultimate ruin probability. People discuss the discrete-time model is a composite of two models, this article from the following promotion: on the one hand, due to the the classical discrete risk model is single insurance model has some limitations. In this paper, it is from reality, combined with the ideology of the existing literature, a new insurance risk model, with a Poisson distribution, binomial distribution to fit the two types of insurance claims and premiums came the moment using the martingale method gives the probability of bankruptcy. On the other hand this paper, we consider the real interest rate factors and investment factors, given two kinds of factors of two discrete insurance bankruptcy model, respectively, discussed the problem of the insurance company bankruptcy probability reflects the interest and investment income the bankruptcy probability Extension relevant conclusions. The most typical in the continuous-time model compound Poisson model, founded in 1905 by Lundberg. This article has been studied from the following three aspects: First, by using a more general point of the process, Cox process instead of the Poisson process to describe the number of claims; Markov jump process more scientific approach to describe the premium income, that is, with Markov rates instead of constant rate; consider the uncertainty of the premium income, to characterize the Brownian motion. Such multiple risk model, the use of stochastic theory to discuss their bankruptcy probability estimates of the upper and lower bounds and gives concrete expression. Finally, the actual life insurance, annuities negative risk model in this article also made some improvements Poisson process to fit the premium income reached one pair of Poisson risk model, straightforward the bankruptcy probability Lundberg inequality martingale argument but also to give it to meet the expression. Finally, a summary and further research.

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