论文标题
两种估计Cox-Ingersoll-Ross过程漂移参数的估计方法：连续观测
Two methods of estimation of the drift parameters of the Cox-Ingersoll-Ross process: continuous observations
论文作者
论文摘要
我们考虑$ dr_t =（a -b r_t）dt +σ\ sqrt {r_t} dw_t $的随机微分方程，其中$ a $，$ b $和$σ$是正常数。该解决方案对应于Cox-ingersoll-ross过程。我们通过连续观察样本路径$ \ {r_t，t \ in [0，t] \} $来研究未知漂移参数$（a，b）$的估计。首先，我们证明了最大似然估计器的强一致性。由于此估计器仅在$ 2A>σ^2 $的情况下定义明确，因此我们提出了另一个估算器，该估计器对所有正$ a $ a $，$ b $，$σ$都定义并且强烈一致。估计器的质量通过仿真结果说明。
We consider a stochastic differential equation of the form $dr_t = (a - b r_t) dt + σ\sqrt{r_t}dW_t$, where $a$, $b$ and $σ$ are positive constants. The solution corresponds to the Cox-Ingersoll-Ross process. We study the estimation of an unknown drift parameter $(a,b)$ by continuous observations of a sample path $\{r_t,t\in[0,T]\}$. First, we prove the strong consistency of the maximum likelihood estimator. Since this estimator is well-defined only in the case $2a>σ^2$, we propose another estimator that is defined and strongly consistent for all positive $a$, $b$, $σ$. The quality of the estimators is illustrated by simulation results.
