Two methods of estimation of the drift parameters of the\n Cox-Ingersoll-Ross process: continuous observations
Анотація
We consider a stochastic differential equation of the form $dr_t = (a - b\nr_t) dt + \\sigma\\sqrt{r_t}dW_t$, where $a$, $b$ and $\\sigma$ are positive\nconstants. The solution corresponds to the Cox-Ingersoll-Ross process. We study\nthe estimation of an unknown drift parameter $(a,b)$ by continuous observations\nof a sample path $\\{r_t,t\\in[0,T]\\}$. First, we prove the strong consistency of\nthe maximum likelihood estimator. Since this estimator is well-defined only in\nthe case $2a>\\sigma^2$, we propose another estimator that is defined and\nstrongly consistent for all positive $a$, $b$, $\\sigma$. The quality of the\nestimators is illustrated by simulation results.\n
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