The Properties Of The Bayesian Estimation Of The Entropy Risk Metric Under The Exponential-gamma Model

In recent years,under the background of financial globalization and liberalization,financial risk has become the common concern of financial circle and regulator both here and abroad.Risk measurement is the most important and core part of risk management.It is of great significance to study the risk measurement for the effective management of risk and the construction of financial system in the international background of financial liberalization.With the deepening of the research,the researchers found that VaR has its limitations in many situations.In order to compensate for these limitations,people gradually began to study and put forward other risk measures,such as coherent risk measure,CVaR,TVaR,spectral risk measure,convex risk measure,entropy risk measure,coherent entropy risk measure etc..In financial mathematics,entropy risk measurement is a typical convex but uncoherent risk measure.And if the utility function is given,it can be applied to the utility maximization problem.Risk is the uncertainty,we need to study the uncertainty.In fact,the distribution of the random variable X depends on certain risk parameters ?,so we need to estimate the parameters,at the same time,we need to study the limit properties of the parameters.There are many estimation methods,such as maximum likelihood estimation,Bias estimation,nonhomogeneous reliability estimation,homogeneous reliability estimation,and there are also many limit properties of estimate,such as the large deviation principle,moderate deviation principle,strong consistency,asymptotic normality.Bayesian estimation is one of the most commonly used estimators,and the consistency and the large deviation principle are the most commonly limit properties.In many distribution,exponential distribution and gamma distribution are continuous distribution of probability theory,they have very close contact with some other important distribution,so the analysis of entropy risk measure under the exponential gamma model has a very important significance.In this paper,we mainly verify the consistency of the Bayesian estimation of the entropy risk measure under the exponential gamma model,and then give the large deviation principle for the Bayesian estimation of the entropy risk measure under the exponential gamma model.The structure of the article is as follows:The first chapter analyzes the research background and current situation of risk measurement and large deviation theory,and introduces the value and significance of the research,which leads to the main content of this paper.The second chapter mainly introduces some basic theories related to the article.First,the large deviation principle,the contraction principle,the Gartner-Ellis theorem,the central limit theorem,the Delta Method,the Bayesian estimator are given.Secondly,we give the definition and properties of exponential distribution and gamma distribution.The third chapter mainly introduces several common risk measure.Firstly,the definition and properties of risk measure,convex risk measure and consistent risk measure are given.Then the definition and properties of VaR,CVaR,TVaR and entropy risk measurement are given.The fourth chapter is the main results of this paper.Ih the Bayesian frame,the entropy risk measure model is established based on the exponential gamma model,making full use of the existing information to estimate the entropy risk measure.At first,we give the consistency of Bayesian estimation of entropy risk measurement under the exponential gamma model,and then give the large deviation principle of Bayesian estimation of entropy risk measure under the exponential gamma model.The fifth chapter is the summary and some expectations.