Three stochastic models for order book dynamics

In this dissertation, we study three stochastic models for order book dynamics. We first consider a double-ended queue with renewal arrivals where buyers and sellers arrive to conduct trades. Because the analytical results of the limiting behavior of the double ended queue is intractable except in very special cases, we apply the diffusion approximation method. We find that the queue length process of the double-ended queue converges to an asymmetric Ornstein-Uhlenbeck process with drift. We use simulation to evaluate the goodness of our approximations. Next we consider the double-ended queue where the arrival processes of the buyers and sellers are state-dependent. We assume that traders arrive at the queue according to a phasetype renewal process (PH-renewal process), and an arriving trader is a buyer or a seller according to state-dependent probabilities. We derive an explicit algorithm to compute the limiting distribution of this double-ended queue. We study two special cases withDoctor of Philosoph