| Under the background of economic globalization, the financial industry has developed rapidly. But at the same time, it brings some risk problems. The risk measure can describe effectively the quantitative characterization of financial markets, and predict the future risk. Large deviation principle is one of the hot topics in the study of risk measure problems, therefore it is important significance. This paper mainly presents the asymptotic properties of estimation for the VaR, CVaR and entropic risk measure under the condition of normal distribution, by using the contraction principle in large deviation principle. We also present the asymptotic properties of entropic risk measure under the condition of Laplace distribution by using the Delta method.This thesis is organized as follows:In the first chapter, we introduce the background of the research, the developments of risk measure theory and large deviation theory, then we display the major works of this article.In the second chapter, we mainly introduce basic theoretical knowledge. Firstly, we review large deviation principle, moderate deviation principle, Hadamard differentiable, Delta method and contraction principle in large deviation theory. Then we provide the definitions of normal distribution, Laplace distribution, the relationship between them.In the third chapter, we mainly introduce several common risk measures. First we introduce the definitions and properties of risk measure, convex risk measure, and coherent risk measure. Then we give the definitions and properties of VaR, CVaR, entropic risk measure.In the fourth chapter, we present the main results of the article. This article mainly studies the asymptotic behavior of the estimations of VaR, CVaR and entropic risk measure under the condition of normal distribution. We also study the limit properties of the estimation for the entropic risk measure under the condition of Laplace distribution.The fifth chapter draws the conclusion and a view of further works. |
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