Several Studies On Heavy-tailed Phenomena In Insurance And Finance

Heavy-tailed phenomena are no longer strange for us, they appear in almost all areas. For example, the claim amount of insurance companies, financial time series data, network traffic, natural meteorological data, and most of the human behavioral data’s distribution patterns show leptokurtic features. Extreme events, which are extreme form of heavy-tailed phenomena, are those unexpected events that, if happen, often result in a huge impact, even have extremely serious consequences. Heavy-tailed phenomena can be described by the distribution of heavy-tailed. Heavy-tailed distributions are roughly those whose tails decay to zero slower than at an exponential rate. Stable Pareto distribution, similar to the front-exponential&end-power-law distribution of reality, has a better fitting effects to extreme events.This paper discusses around the heavy-tailed phenomena from various angles. Firstly, we talk about the heavy-tailed phenomena in the fields of insurance and finance. In the field of insurance, we discuss about large claim affectting sound operating of insurance company, and campare the probability of bankruptcy when claim amout is exponetiak Pareto、Frechet or Weibull distribution. In the field of finance, we discuss the defect of traditional method in estimating of VaR, and regard extreme value theory as a better method to estimate VaR under heavy-tailed occasion. Then, we discuss the heavy-tailed phenomena from different theoretical perspectives (liquidity black hole perspective, non-linear perpective), and research the occurrence mechanism of heavy-tailed phenomena by mechanism of positive feedback and non-linear. Finally, we introduce the methods of statistical description of heavy-tailed phenomena, fit the stable pareto distribution to the daily returns of Shanghai composite index and get a good fitting effect.The paper is divided into six chapters. The content of it is as follows:The first chaper introduces the background and significance of this paper, elaborates the research content and research methods, and illustrates the innovations and inadequacies.The second chapter discusses about large claim affectting sound operating of insurance company, campares the probability of bankruptcy when claim amout is exponetiah Pareto、Frechet or Weibull distribution.The third chaper discusses the defect of traditional method in estimating of VaR, and regards extreme value theory as a better method to estimate VaR under heavy-tailed occasion.The4th chapter discusses the heavy-tailed phenomena from different theoretical perspectives(liquidity black hole perspective, non-linear perpective), and researches the occurrence mechanism of heavy-tailed phenomena by mechanism of positive feedback and non-linear.The5th chapter introduces the methods of statistical description of heavy-tailed phenomena.The6th fits the stable Pareto distribution to the daily returns of Shanghai composite index and gets a good fitting effect...