Arbitrage, market microstructure and the limit order book

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In the first part we study arbitrage opportunities in diverse markets. The construction of such markets is based on an absolutely continuous but non-equivalent measure change which implies the existence of instantaneous arbitrage opportunities. In the second part, we look at a model for the limit order book. Here we deal with the issue of how to construct a framework for order arrival, storage, cancellation and execution. It turns out that the limit order book will be the difference of two doubly stochastic Poisson processes at every point in time. We investigate properties of the bid-ask spread, a new type of options, the average order book in the long-run as well as cancellation of orders using ideas from queuing theory. Finally, we also look at an extension to a large trader model. The third part deals with a dynamic market microstructure model, in which a strategic market maker competes with an informed trader. We include the presence of noise traders and limit order traders in our setup. The resulting recursive equations lead to various economic interpretations. Our framework is general enough to obtain several well-known models in a straightforward way.