在帕累托模型中风险度量的统计分析

在帕累托风险模型中,该文研究了在险价值及其相关风险度量的关系,给出了在险价值、期望短缺、尾条件期望、条件在险价值等风险度量的计算方法; 进而,利用极大似然法和矩估计法得到了这些风险度量的估计,证明了估计的相合性和渐近正态性; 最后利用数值模拟的方法验证了在不同样本下估计的收敛速度.

The Statistical Analysis of Risk Measure in Pareto Risk Model

In the Pareto risk model,the relationship between the VaR and its associated risk measure is discussed,and the expressions of value at risk,expectation shortfall,tail value at risk and conditional value at risk are given.Furthermore,the estimation of these risk measures is obtained by using the maximum likelihood method and the moment estimation method,and the consistency and asymptotic normality of those estimators are also proved.Finally,the numerical simulation method is used to verify the convergence rate under different samples.