Ph.D. Defense: Haipeng Gao
Ph.D. Thesis Defense
Friday, March 29th, 2019
112 Hanes Hall
Bayesian Inference for Stochastic Cusp Catastrophe Model
(Under the direction of Chuanshu Ji)
In modern financial econometrics, diffusion processes have been broadly used to model the stochastic behavior of economic variables such as stock prices, interest rates, and exchange rates. Well-known models such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross (CIR mdoel), all assume that the underlying state variables follow diffusion processes. If one believes that the observed time-series are generated according to some parametric specification, developing rigorous statistical methods to calibrate the underlying model to measured observations has become a considerable subject of the field.
The thesis considers cusp model, one of the elementary catastrophe models studied in catastrophe theory. The research problem of this thesis is to develop an accurate and computationally feasible parameter estimation algorithm based on Bayesian principle that can be implemented in absence of an exact transition distribution for cusp model using discretely sampled observations. The problem can be further specified as parameter estimations using complete observations and using partial observations. Accuracy and efficiency of the approach are demonstrated and examined in a series of simulation-based studies that consists of both trajectory simulations and parameter estimations. We extend the developed algorithm and apply it to Bayesian hierarchical modeling and time-varying parameter setting.