Diffusion Scaling of a Limit-Order Book: The Asymmetric Case

This thesis is the extension and generalization of the thesis of Christopher Almost. Following a simplified specification of the dynamics proposed in Cont, Stoikov, and Taireja where orders arrive according to Poisson processes whose intensities depend on the relative distance between price of arriving and opposite best price, we show that the heavy-traffic scaled sequence of LOB models converges to a simple model where the scaled number of orders at each price level follows either a diffusion or a jump-diffusion process.