The model of nonlinear differential systems with impulsive effect on random moments is brought forward in this paper. Then, sufficient conditions for (uniform, uniform and ultimate, and uniform and uniformly ultimate) p?moment boundedness of the systems are presented. Finally, an example is discussed to show applications of two obtained results.
The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.
ZHANG Shibin,ZHANG Xinsheng & SUN Shuguang School of Management, Fudan University, Shanghai 200433, China
The existence and uniqueness in mean square of solutions to certain random impulsive differential systems is discussed in this paper. Cauchy-Schwarz inequality, Lipschtiz condition and techniques in stochastic analysis are employed in achieve the desired results.
