This thesis covers three topics related to stock market microstructure in financial engineering.

Survival analysis has been a useful tool in statistics, among which accelerated failure time model and linear transformation model with given error distribution are popular. However, the error distribution is usually unknown in reality. In the first topic, we choose to develop a new linear transformation model with the error term belonging to a generalized gamma distribution family, and propose an iterative algorithm to calculate the maximum likelihood estimates of the model. We conduct simulation studies to evaluate the finite sample performance of our model. We also fit our model to a real stock dataset of limit order execution times. Cross validation is carried out to illustrate...[ Read more ]

This thesis covers three topics related to stock market microstructure in financial engineering.

Survival analysis has been a useful tool in statistics, among which accelerated failure time model and linear transformation model with given error distribution are popular. However, the error distribution is usually unknown in reality. In the first topic, we choose to develop a new linear transformation model with the error term belonging to a generalized gamma distribution family, and propose an iterative algorithm to calculate the maximum likelihood estimates of the model. We conduct simulation studies to evaluate the finite sample performance of our model. We also fit our model to a real stock dataset of limit order execution times. Cross validation is carried out to illustrate the advantage of our model compared to accelerated failure time model.

Reinforcement learning techniques have been applied to many fields in financial engineering, such as optimal liquidation and market making. In the second topic, we formulate the optimal liquidation problem in the framework of finite horizon reinforcement learning and propose to use a neural network to approximate the optimal state-value function and give the probability of choosing each action in a given state. The architecture of the neural network is designed to extract significant features from the limit order book and market maker's private state variables, and to perform dimension reduction. Empirical studies are carried out to demonstrate that our reinforcement learning based optimal liquidation strategy can be profitable.

Traditional market making models take advantage of stochastic dynamic programming and stochastic control theory, where bid and ask prices are dynamically determined to maximize some long term objectives such as expected profits or expected utility of profits. However, most models in the literature fail to consider the price impact of market orders on the mid-price of the underlying asset. Their assumption that market orders arrive at the financial market according to Poisson process does not take the clustering and mutually exciting effects of market buy and sell order arrivals. In the third topic, we propose a new market making model where incoming market orders cause random jumps on the mid-price and we model the arrival process of market orders as Hawkes process. Simulation results show that the new market making strategy can be profitable.