I propose a continuous-time model of price formation in a market where trading is conducted according to a limit-order book. Strategic liquidity traders arrive randomly in the market and dynamically choose between limit and market orders, trading off execution price with waiting costs. I prove the existence of a Markov equilibrium in which the bid and ask prices depend only on the numbers of buy and sell orders in the book, and which can be characterized in closed-form in several cases of interest. My model generates empirically verified implications for the shape of the limit-order book and the dynamics of prices and trades. In particular, I show that buy and sell orders can cluster away from the bid-ask spread, thus generating a hump-shaped limit-order book. Also, following a market buy order, both the ask and bid prices increase, with the ask increasing more than the bid-hence the spread widens.

We compare the optimal trading strategy of an informed speculator when he can trade ahead of incoming news (is “fast”), versus when he cannot (is “slow”). We find that speed matters: the fast speculator's trades account for a larger fraction of trading volume, and are more correlated with short‐run price changes. Nevertheless, he realizes a large fraction of his profits from trading on long‐term price changes. The fast speculator's behavior matches evidence about high‐frequency traders. We predict that stocks with more informative news are more liquid even though they attract more activity from informed high‐frequency traders.

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Abstract. Equivariant elliptic cohomology with complex coefficients was defined axiomatically by Ginzburg, Kapranov and Vasserot [9] and constructed by Grojnowski [10]. We give an invariant definition of complex S 1 -equivariant elliptic cohomology, and use it to give an entirely cohomological proof of the rigidity theorem of Witten for the elliptic genus. We also state and prove a rigidity theorem for families of elliptic genera.

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