Never selling stocks is optimal for investors with a long horizon and a realistic range of preference and market parameters, if relative risk aversion, investment opportunities, proportional transaction costs, and dividend yields are constant. Such investors should buy stocks when their...

In a market with price-impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long-term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities...

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...

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 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...

This paper studies the equilibrium price of an asset that is traded in continuous time between N agents who have heterogeneous beliefs about the state process underlying the asset's payoff. We propose a tractable model where agents maximize expected returns under quadratic costs on inventories...

Optimal execution and trading algorithms rely on price impact models, like the propagator model, to quantify trading costs. Empirically, price impact is concave in trade sizes, leading to nonlinear models for which optimization problems are intractable and even qualitative properties such as...