Least Square Estimation Of Drift Term In Stable JCIR Model

Cox-Ingersoll-Ross(CIR)is a financial mathematical model describing the evolution of interest rate,stationary CIR model is a stationary process-driven CIR model,It is also a special continuous state branching process with migration,CIR model and stationary CIR model have been widely used in mathematical finance.JCIR is a diffused CIR model with jump,Stationary JCIR model is a JCIR model driven by stationary process.Compared with the CIR model and the stationary CIR model,JCIR model contains more possible jumps.The classical JCIR model is a common building block of various models in mathematical finance.The Stationary JCIR model is a special case of the short-term interest rate model,which can more accurately describe the randomness of interest rate data changes Therefore,the study of stationary JCIR model has more important practical significance.In this dissertation,the least squares estimation of drift coefficients in stationary JCIR models with small perturbations is studied.Firstly,the moment of stationary JCIR model is established,and then the stationary JCIR model is obtained by It(?)'s formula and Gronwall's lemma According to the C_r inequality,the upper bound of the r-moment of the stationary JCIR model is finite.Then research The least squares estimation of the drift coefficient under small disturbance is studied,and the least squares estimation of b and ? is obtained by in-troducing the contrast function Estimation.Finally,using Levy-It(?) representation,Markov inequality,error expression between estimator and true value,The asymptotic behaviors with more accurate estimates are established,such as the central limit theorem,deviation inequal-ity,large deviation principle and medium deviation principle.