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Ruin Theory with Risky Investment and Subexponential Claims

Author: ChenYiQing
Tutor: XieXiangSheng
School: Guangdong University of Technology
Course: Management Science and Engineering
Keywords: Asymptotic Heavy-tailed Subexponential distribution Venture Capital Probability of ruin
CLC: F224
Type: Master's thesis
Year: 2005
Downloads: 112
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Abstract


This thesis is dedicated to research in venture capital and the heavy-tailed risk occasions asymptotic ruin probability. A total of six chapters. In the first chapter, we briefly review some of the recent research literature and the research techniques and characteristics. In the second chapter, we introduce some important heavy-tailed distributions, especially subexponential. Throughout a basic assumption: insurance risk (loss variable) or financial risk (the discount factor) is heavy-tailed. The third to the sixth chapter is the main part of this paper, we give the results and relevant certificates. The third chapter in the financial environment for the insurance industry to introduce a random and defines a simple asymptotic formula after infinite time ruin probability, we get a finite time ruin probability. The results improve the work of Tang and Tsitsiashvili (2003), in particular, our results solve this critical occasion with the same heavy-tailed insurance risk and financial risk. Compared to the with Tang and Tsitsiashvili (2003) work, we proved to be more concise and more intuitive. In the fourth chapter, we further the results of the previous chapter extended to infinite time ruin probability of occasions. We get the results of the previous chapter the results seem consistent with the limited time. It is worth mentioning, we created some new skills proved, these results are very useful in the tail behavior when dealing with infinite random series. However, in the process of proof, we have to use Vervaat (1979) some very profound results. In the fifth chapter, we study the the subexponential weighted random variables and their maximum general probabilistic model. Undoubtedly, these subtle tail probability behavior frequently in many areas including the application of probability the bankruptcy theory within the plays an important role. By using famous Matuszewska index skills and Davis and Resnick (1988), we derive a weighted random variables and their maximum asymptotic formula. By selected non-randomly right values, our results can be directly applied to the bankruptcy theory, given infinite time ruin probability constant interest rates and subexponential claims occasions, a simple asymptotic estimate. In the last chapter, we try to promote the results of the previous chapter to a random weights occasions the occasion to deal with more difficulty. The advantage of the work in this chapter derivation a random weighted and its maximum asymptotic estimate, we do not make any requirements dependencies between random weights; shortcomings, we must assume that the claim amount to obey the Pareto distribution and random weights has upper bound. However, in the application of bankruptcy theory (especially) these restrictions are very reasonable.

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CLC: > Economic > Economic planning and management > Economic calculation, economic and mathematical methods > Economic and mathematical methods
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