Statistical Analysis Of Risk Measurement Based On Value At Risk

The risk arises from the uncertainty of future events.From a mathematical point of view,it indicates the possibility of various outcomes.It is often expressed in probability statistics by the non-negative random variable X.In risk management,how to conduct appropriate risk measure-ment is one of the important tasks of financial risk managers.Risk measurement,also known as risk estimation,is the quantitative analysis and description of risks based on the identification of risks.In other words,we give the quantitative analysis and prediction and determine the proba-bility of occurrence of risk accidents by using probabilistic and mathematical statistics tools based on the analysis of past loss data.Through the risk measurement,a more accurate loss probability can be calculated,which can enable risk managers to eliminate the loss uncertainty to a certain extent.And then the more serious losses of risk are focused.This paper studies the statistical properties of value at risk and the related risk measurement.In the second chapter,we introduce the definition and properties of risk measurement.By introducing a consistent risk measurement,we state the relationship and properties of value at risk and related risk measures.In the third chapter,under the Pareto risk model,the relationship between the value at risk and related risk measurement is studied,and the calculation methods of risk measurement such as value at risk.expected shortfall,tail condition expectation,and conditional risk value are given.Then,the max-imum likelihood method and moment estimation method are used to obtain the estimates of these risk measurements,and the consistency and asymptotic normality of the estimators are proved Finally,the convergence rate of the estimation under different samples is verified by numerical sim-ulation.The fourth chapter establishes the Bayesian model,we research the relationship between the value of risk and its related risk measures,and get the Bayesian estimates of risk measures such as risk value,expected shortfall,tail condition expectation,and conditional risk value.The consistency and asymptotic normality of the estimation are proved in the exponential risk model Finally,the convergence rate of the estimation under different samples is verified by the numerical simulation method.In the fifth chapter,we establish the Exponential risk for risk measurements and discussed the credibility estimates of risk measurement combined with the classical credibility theory.The estimates and consistency are compared and verified for these estimates.