Study On Capital Allocation Based On Tail Risk Measure

In utility theory,the Expected Shortfall(ES)risk attitude is expressed based on the linear utility function,while ES and capital allocation based on ES are difficult to express the complex non–linear relationship in reality.Therefore,we are inspired by the relevance between ES based capital allocation and ES.The ES based capital allocation model is extended to the general case.The non–neutral risk attitude is expressed by the non–linear Young function family,and the non–linear contribution of risk to the total risk event is evaluated according to different risk attitude,instead of the ES based capital allocation model to deal with the non–linear situation.On the one hand,based on the definition of ES capital allocation and Orlicz norm,this paper studies the extension of ES based capital allocation,puts forward the capital allocation model based on Orlicz risk measure,and solves the nonparametric estimation problem of capital allocation based on Orlicz risk measure by using the estimation equation method.First,we start from the definition of ES capital allocation,and combine the definition of Orlicz norm,a capital allocation model based on Orlicz risk measure is established.Secondly,the capital allocation based on Orlicz risk measure is estimated by the estimation equation.The strong consistency and asymptotic normality of the estimation are obtained,and then the asymptotic normal confidence interval is obtained.Finally,the sample performance of the estimation method under different confidence levels and sample sizes is simulated by R software.On the other hand,we use the method of estimating equation to solve the problem of nonparametric estimation of capital allocation of Haezendonck–Goovaerts risk measure(HGRM),and get the empirical estimation of capital allocation based on HGRM,the estimation equation estimation and their strong consistency and asymptotic normality.In this paper,we give the definition of HGRM's capital allocation.The consistency and asymptotic normality of empirical estimates are proved,and the asymptotic normal confidence interval is obtained.In some specific problems,the estimation of threshold value is also concerned.In order to give the estimation of capital allocation and threshold value based on HGRM at the same time,the joint estimation equation of capital allocation and threshold value based on HGRM is established from the definition of capital allocation based on HGRM.The joint estimator is obtained,and the large sample property of the estimator is also proved.The influence of sample size of capital allocation based on HGRM estimation is analyzed by numerical simulation.