Parameters Estimation Of The Stable CIR Model In Random Environments

In the field of financial mathematics,the Cox-Ingersoll-Ross(CIR)model focuses on describing the evolution of interest rates.And the term structure is treated as a stochastic process.The stable CIR model(also known as the SCIR model)is a CIR model driven by a stable process.Currently,there are many studies on the parameter estimation of CIR and the stable CIR models.In this thesis,the stable CIR model in the random environments are based on the stable CIR model with the stochastic integration driven by Brownian motion.Compared with the CIR model and the stable CIR model,the stable CIR model in the random environments contains a stochastic environment and more possible jump terms than the CIR model and the stable CIR model,which can more accurately describe the change of interest rate term.It can be seen that it is important to study the parameter estimation of the drift term the stable CIR model in the random environments.The estimation of the drift term in the stable CIR model in the random environments have good practical significance and wide application prospects.In the stable CIR model under random environments,this thesis focuses on the least squares estimation problem under small perturbations.Firstly,the specific mathematical expressions of the stable CIR model in the random environments and its moment estimation are given,and then the r order moments of the stable CIR model in the random environments are proved to be finite by using the It(?) formula and Gronwall’s Lemma,the r order moments of the stable CIR model model in the random environments are proved to be finite.The upper bound of the r order moments of the stable CIR model in the random environments are also finite by using the C_rinequality and Burkholder-Davis-Gundy(BDG)inequality.Then,by introducing the comparison function,we mainly study the least-squares estimation of the drift coefficients of the stable CIR model in the random environments under small perturbations,and the least-squares estimates of b,are given.Finally,according to the L(?)vy-It(?) representation,the BDG inequality,Markov’s inequality and the error of the parameter estimates and the true value of The asymptotic behavior of the more accurate estimates and their important proof procedures are given.