Second order approximations for limit order books

We derive a second order approximation for an infinite dimensional Markovian limit order book model under two different scaling regimes. In the first case we suppose that price changes are really rare, yielding a constant... [ view full abstract ]

We derive a second order approximation for an infinite dimensional Markovian limit order book model under two different scaling regimes. In the first case we suppose that price changes are really rare, yielding a constant first order approximation for the price and a measure valued SDE driven by an infinite dimensional Brownian motion in the second order approximation of the volume process. In the second case we use a slower rescaling rate, which leads to a non-degenerate first order approximation and gives a PDE with random coefficients in the second order approximation for the volume process.