Research On The Asymptotic Behavior Of Several Types Of Risk Measurement Estimation Under The Exponential Gamma Model

Risk control is an important topic in investment.The research on VaR,CVaR in risk management is relatively concentrated.VaR comprehensively considers the size of expected risk and the probability of its occurrence and we can avoid market risk by calculating VaR beforehand.CVaR takes more tail risk than VaR into account and has an obvious advantage in optimizing its portfolio.In this paper,we focus on the asymptotic properties of Bayesian estimates of VaR and CVaR based on exponential gamma models,including strong consistency,asymptotic normality,large deviation principle and moderate deviation principle.This paper is mainly divided into the following chapters:The first chapter mainly introduces the relevant background and development status of the two related risk measures,and gives the main research results of this paper.Chapter 3 and chapter 4 are the main research results.We consider several asymptotic behaviors of Bayesian estimates of VaR and CVaR.Firstly,we prove that the Bayesian estimates of CVaR is the strong coincidence estimate of CVaR.Secondly,we prove that the Bayesian estimate of CVaR satisfies asymptotic normality.Finally,we consider the large deviation principle and the moderate deviation principle of Bayesian estimates of VaR and CVaR,and obtain the related asymptotic behavior.The fourth chapter is mainly about the application and numerical simulation of the conclusions in the third chapter.Firstly,we calculate and simulate the confidence interval,the upper confidence limit and the lower confidence limit.The simulation results show that when the parameters are fixed,the interval length is negatively correlated with the number of simulations,and when the number of simulations is fixed,the interval length is positively correlated with the parameters,which is consistent with the theoretical results.Secondly,we simulate the central limit theorem and compare the Bayesian estimates of CVaR,VaR with the ordinary quantile method.It is found that the Bayesian estimates's error of the two kinds of risk measures is smaller.Finally,we simulate the tail probability of Bayesian estimate of VaR measure,and verify the correctness of the moderate deviation principle of VaR Bayesian estimation.In the fifth chapter,we summarize this paper and put forward further research.