Asymptotic Behavior Of Expectile Estimator Based On Entropic Function

Economic globalization promotes the vigorous development and expansion of financial market,and various countries gradually realize the necessity of financial risk management.After the subprime mortgage crisis in the United States,the world is now facing an economic crisis brought about by the COVID-19.Therefore,in such an environment,financial risk management is becoming more and more important.Among them,financial risk measurement,as an important part,plays a basic and key role in the process of measuring the market risk of financial assets,statistical models are usually used to measure the value at risk.In this thesis,entropic loss function and heteroscedasticity terms are introduced into the classical expectile model.Specifically,firstly,the expectile based on entropic loss function is proposed,and the consistency and central limit theorem of the expectile estimators based on entropic loss function are studied,and the results are verified by numerical simulations;Secondly,this thesis establishes two linear heteroscedasticity models of expectile based on entropic loss function,studies the problems of parameter estimation under the two linear models,and obtains the asymptotic behaviors of parameter estimators,including consistencies and central limit theorems.This thesis mainly includes the following four chapters:The first chapter mainly introduces the research background,significance and research status of expectile in financial risk management,and expounds the content arrangement and innovation of the thesis.The second chapter mainly introduces the preparation knowledge of the thesis.It includes the definitions of value at risk and expected loss,the concept of expectile and its relationship with common risk measures,as well as some necessary properties,including the properties of Dirac delta function.In the third chapter,the expectile based on entropic loss function is proposed,and the first-order conditions satisfied by the expectile are obtained.Secondly,the consistency and asymptotic normality of the expectile based on entropic loss function are studied by numerical simulations.In the fourth chapter,two linear heteroscedasticity models of expectile based on entropic loss function are studied.Firstly,this chapter considers the linear ARCH model based on the expectile of entropic loss function,gives the estimators of the model parameters,and obtains the consistency and asymptotic normality of the estimators;Secondly,this chapter introduces GARCH model as the error term,considers the linear GARCH model based on the expectile of entropic loss function,gives the estimators of model parameters,and obtains the consistency and asymptotic normality of the estimators.Finally,the main work of this thesis is briefly summarized,and some problems which are worthy of further research are discussed.