We derive the process followed by trading volume, in a market with finite depth and constant investment opportunities, where a representative investor, with a long horizon and constant relative risk aversion, trades a safe and a risky asset. Trading volume approximately follows a Gaussian,...

We find asymptotically optimal trading policies for long-term investors with constant relative risk aversion, in a multiple-assets market where expected returns and covariances are constant, and the execution price of each asset is linear in the trading intensities of all assets. Trading towards...

A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so, we allow for general dynamics of the mid price, the...

We study how short-term informational advantages can be monetized in a high-frequency setting, when large inventories are explicitly penalized. We find that if most of the additional information is revealed regardless of the high-frequency traders' actions, then fast inventory management allows...

We study optimal investment with multiple assets in the presence of small proportional transaction costs. Rather than computing an asymptotically optimal no-trade region, we optimize over suitable trading frequencies. We derive explicit formulas for these and the associated welfare losses due to...

We study optimal execution with "self-exciting" price impact, where persistent trades not only incur price impact but also increase the execution costs for successive orders. This model is motivated by an equilibrium between fundamental sellers, market makers, and end users. For risk-neutral...

We show that wealth processes in the block-shaped order book model of Obizhaeva/Wang converge to their counterparts in the reduced-form model proposed by Almgren/Chriss, as the resilience of the order book tends to infinity. As an application of this limit theorem, we explain how to reduce...