The asymptotic behaviors and applications of the Bayesian estimator for the tail value at risk on Pareto-Gamma risk model is helpful to make statistical inference on risk measure, so that venture investors can take corresponding measures to avoid risks in time. Firstly, by constructing Bayesian hypothesis of Pareto-Gamma risk model, the Bayesian estimator for tail value at risk is given, then by using classical large deviation theory, moderate deviation theory and Delta method, the asymptotic behaviors of the Bayesian estimator for tail value at risk is given out, including the asymptotic normality, large deviation principle and moderate deviation principle. Secondly, the specific applications of the moderate deviation principle of the Bayesian estimator for tail value at risk in statistical hypothesis testing are given, and the asymptotic behaviors of the type I error and power function are obtained. Finally, the simulation methods are given to investigate the confidence interval and interval coverage of the tail value at risk, and the standardized histogram and kernel density estimation curve of the Bayesian estimator of tail value at risk are drawn for different sample sizes, which basically coincide with the standard normal distribution density function curve, thus the asymptotic normality of the estimator is verified. At the same time, the stochastic simulation of the tail probability of the tail value at risk is given to show that the tail probability approaches zero at a certain speed when the sample size is sufficiently large, thus the moderate deviation principle of the estimator is verified.
