## A Markov model of a limit order book: thresholds, recurrence, and
trading strategies

Frank Kelly, joint work with
Elena Yudovina.

In this talk we discuss an analytically tractable model of a limit order
book where the dynamics are driven by stochastic fluctuations between
supply and demand. The model has a natural interpretation for a highly
traded market on short time-scales where there is a separation between the
time-scale of trading, represented in the model, and a longer time-scale on
which fundamentals change.
We describe our main result for the model, which is the existence of an
explicit limiting distribution for the highest bid, and for the lowest ask,
where the limiting distributions are confined between two thresholds. Fluid
limits play an important role in establishing the recurrence properties of
the model.

We use the model to analyze various high-frequency trading strategies (for
example market-making, sniping and mixtures of these), and comment on the
Nash equilibria that emerge between high-frequency traders when a market in
continuous time is replaced by frequent batch auctions.

Keywords: limit order book, queueing, fluid limit, high-frequency trading,
Nash equilibrium

Paper:

A
Markov model of a limit order book: thresholds, recurrence, and trading
strategies

*
Frank Kelly and Elena Yudovina*

Mathematics of Operations Research, to appear