Estimation Of Two Kinds Of Entropy Risk Measure And Research On Asymptotic Behavior

In the background of the financial globalization, financial risks management is a hot topic in financial institutions and financial supervisors. More and more attention is paid to the financial risk management. Risk measure is the core of financial risk management, so the research of risk measure is of great significance. So far, VaR, CVaR, SRM, EVaR, entropic risk measures and other risk measures have been proposed by domestic and foreign experts and scholars, providing a reliable theoretical basis for risk management. In recent years, lots of researches have been made on the combination of information entropy and the theories of risk measures. In this paper, we mainly study several deviations and asymptotic behaviors of convex and coherent entropy risk measures of the compound Poisson process by introducing parameters depending on time.This thesis is organized as follows:In chapter 1, we first introduce the significance of the research and the development of risk measure theory, and then display the major works of this thesis.Chapter 2 recalls some related theoretical contents. Firstly, we introduce the large deviation principle, Varadhan theorem and Gartner-Ellis theorem. Then we present the definition and properties of the compound Poisson process. Finally, we provide some other properties and proofs, mainly including the mean, variance and exponential moment of compound Poisson process and so on.In Chapter 3, firstly, formulation and comparative analyses are made on the risk measure, convex risk measure and coherent risk measure. Then the definitions and properties of the common risk measure methods of VaR, CVaR, SRM, entropy risk measures and the relationships among them are presented. Finally, we explain the construction method of risk spectrum function through two examples which are exponential risk spectrum and geometric risk spectrum.Chapter 4 is the core of this thesis. By introducing parameters depending on time, we investigate several deviations and asymptotic behaviors of convex and coherent entropic risk measures of the compound Poisson process. To begin with, some estimations and deviations of convex entropic risk measures are provided. Then, one asymptotic behavior of convex entropic risk measure based on the large deviation principle is concluded. On top of that, we provide two asymptotic behaviors of coherent entropic risk measures.Chapter 5 draws the conclusion and a view of further works.