Ornstein-Uhlenbeck过程的参数估计.pdf

Ornstein-Uhlenbeck   Monte Carlo Euler  Ornstein-Uhlenbeck Ornstein-Uhlenbeck Euler Ornstein-Uhlenbeck Ornstein-Uhlenbeck Monte Carlo  Ornstein-Uhlenbeck ℄ Euler ℄ Monte Carlo I Abstract Ornstein-Uhlenbeck process is one kind of diffusion processes,which is widely used in physics and finance. In this paper,I estimate the parameter of it based on the theory of estimating functions via parameter transformation,using a simple and explicit estimating function to estimate one part of the parameter first,and then using the optimal quadratic martingale estimating function for the remaining part of the parameter. Comparing with the maximum likelihood estimator, the new estimator obtaining from this method not only has simple form and need not much computation,but also has good asymptotic properties. In the end,I compare this es- timator with estimators obtained by maximum likelihood and Euler approximation method via Monte Carlo numerical simulation. The paper is of four parts.Chapter one is the introduction.Section one of Chap- ter two introduces the mathematical model of Ornstein-Uhlenbeck process,and explains the physical meaning of the process as well as its parameters.Section two recalls some related basic knowledge and displays some definitions ,suppo- sitions and theories involved in the paper.Chaper three is the main body of the paper.Section one describes the estimator of the process ob