基于在险价值风险度量的信度估计

Credibility Estimation Based on Risk Measure of Value at Risk

在险价值度量（Value—at—Risk）是金融中的一种重要的风险度量方法，被广泛应用于金融、保险等风险管理行业．建立了在险价值的贝叶斯统计模型，利用信度理论的方法将在险价值的估计限定在经验估计的线性函数中，得到了在险价值的信度估计．进而，证明了估计相合性和渐近正态性．最后，利用数值模拟的方法在中等样本容量下验证了估计的收敛速度．

Value-at-Risk （VaR） is an important measure of risk in finance and is widely used in the risk management such as finance and insurance. In this paper, a Bayesian statistical model of VaR is established, and the credibility estimation of VaR is derived by using the credibility theory to constrain the estimation of VaR in the linear function of empirical esti- mation and collective estimation. Furthermore, the consistency and asymptotic normality of credibility estimation of VaR are proved. Finally, the numerical simulation method is used to verify the convergence rate of the estimation under medium sample size.