题目：Affine Jump-Diffusions: Stochastic Stability and Limit Theorems

　　报告人：张晓炜，香港科技大学，助理教授

　　时间：2017年5月11日(周四)15:30~17:00

　　地点：经管院B226

　　报告摘要如下：

　　Affine jump-diffusion (AJD) processes constitute an important class of continuous time stochastic models that are widely used in finance and econometrics. For instance, many classic models in derivative pricing are special cases of AJD processes: the Ornstein-Uhlenbeck (OU) process (i.e. the Vasicek model), the square-root diffusion process, (i.e. the Cox-Ingersoll-Ross model), and the Heston stochastic volatility model. This class of models is flexible enough to capture various empirical attributes such as stochastic volatility and leverage effects. Its affine structure leads to significant tractability both for computing various expectations and probabilities.

　　Most methods for parameter estimation (e.g. maximum likelihood estimation or generalized methods of moments) of this type of processes generally assume ergodicity in order establish consistency and asymptotic normality of the estimator. In this talk, we present several results on the stochastic stability of AJDs. We establish ergodicity of AJDs by imposing a “mean reversion” assumption and a mild condition on the distribution of the jumps, i.e. the finiteness of a logarithmic moment. As a stronger result, exponential ergodicity is proved if the jumps have a finite moment of a positive order. In addition, we prove strong laws of large numbers and functional central limit theorems for additive functional of this class of models. These limit theorems lay solid foundation for parameter estimation methods of AJDs.

　　报告人简介：

　　张晓炜现任香港科技大学工业工程与物流管理系助理教授;2006年从南开大学数学基地班本科毕业后前往美国斯坦福大学深造，并分别与2010年和2011年获得金融数学硕士学位和管理科学与工程博士学位。研究兴趣包括蒙特卡洛方法、仿真优化、稀有事件模拟、金融工程等。