Several Studies On Risk Management Based On Dependent Structure And Heavy-Tailed Risk

In recent years, volatility in financial markets has become increasingly intense, and some of the significant events from financial crisis are more and more frequent. Therefore, there is an urgent call for a more appropriate model to control the risk. At the same time, the phase correlation between financial assets makes the dependent risk become a hot topic in the study of risks.In the field of insurance, ruin theory plays a vital role in risk theory. It studies the risk impact of the insurer solvency from the angle of claim. When we do research on ruin theory, we mainly study the ruin probability, which is a primary indicator of studying the robustness of insurance company. Ruin theory is one of the most important tools for risk management. Through some studies, we can find that it is common phenomenon that the distribution of data is heavy-tailed among many fields, such as finance, insurance, economics, meteorology and so on. Heavy-tailed phenomenon is used to describe some extreme events, that is, some unexpected events which are likely to lead huge impact once they occur, and even have extremely serious consequences. Mention of heavy-tailed, we usually use heavy-tailed to depict. Then, the issue involves two kinds of assumptions:relevant variables have some dependence structures, and investment rate is heavy-tailed. Based on the above assumptions, the article chapter first gives an asymptotically equivalent formula for the finite-time ruin probability of the insurance company which has the independence structure, and elaborates when the other parameters are constant and the change of one of the parameters as to how it has impact on the ruin probability. Therefore, on the basis of the first chapter, we can obtain more instructive conclusions for the actual operations of insurance company. Secondly, based on independency structure the ruin probability of an insurance company with the dependency structure is introduced, and the asymptotically equivalent formula for the finite-time ruin probability with the dependency structure of different progressives is provided.In order to have a specific research on dependent risk, the concept of random sequence is introduced. In the third chapter, several common types of random sequence are introduced as well as the properties of all kinds of sequence and the relationship between each other. Second, the concept of the risk sequence with heavy-tailed risk and ruin probability are combined together in order to study the ruin probability under the meaning of the random sequence. In the fourth chapter, one kind of special random sequence-comonotonicity is studied. In the insurance policies, if the condition is dependent, independence assumption is likely to underestimate the risk of assets. Negative dependency means that the higher one of the insurance policy is, the lower the other claims are. The key result is that if the random variables are extremely dependent, the sum of these variables’ risk will be the greatest. The sum of random variables and its bounds in detail through two practical applications of comonotonicity will be introduced:one is the application of life insurance actuarial; another is the application of in pricing on Asian option. At last, two models of the result of the numerical illustrations and quantitative analysis and the comonotonicity of the two practical applications will be provided respectively.In the last chapter, the extreme events with the dependence structure will be focused. The copula of a multivariate distribution can be considered to describe the dependence structure. In the upcoming studies, we will focus on how to quantify so as to capture the potential of the tail features and the impact of the dependence structure. This chapter introduces the concept of the consistent tool of risk measurement-ES (expected shortfall), and emphatically studies two specific models in the case of extreme events. One is the pricing of insurance contracts, and the result shows when pricing contracts which depend on simultaneous exceedances over high thresholds, knowledge of pairwise correlations and marginal distribution is not sufficient. The other is a perfect storm. ES is used to measure the risk of stock rate. By Monte Carlo simulation the differences between Value at Risk and ES value of different copula structures can be compared. The conclusion that can be drawn from this example is that when considering risk measures which describe the tail of the distribution the choice of the copula representing the dependent structure among the risks is very important. Furthermore, unlike expected shortfall, VaR does not quite reveal the extra risks inherent in a dependent structure with tail dependence.