We study the high-frequency limits of strategies and costs in a Nash equilibrium for two agents that are competing to minimize liquidation costs in a discrete-time market impact model with exponentially decaying price impact and quadratic transaction costs of size θ ≥ 0. We show that, for θ = 0, equilibrium strategies and costs will oscillate indefinitely between two accumulation points. For θ > 0, however, strategies, costs, and total transaction costs will converge towards limits that are independent of θ. We then show that the limiting strategies form a Nash equilibrium for a continuous-time version of the model with θ equal to a certain critical value θ * > 0, and that the corresponding expected costs coincide with the high-frequency limits of the discrete-time equilibrium costs. For θ = θ * , however, continuous-time Nash equilibria will typically not exist. Our results permit us to give mathematically rigorous proofs of numerical observations made in [28]. In particular, we provide a range of model parameters for which the limiting expected costs of both agents are decreasing functions of θ. That is, for sufficiently high trading speed, raising additional transaction costs can reduce the expected costs of all agents.MSC classification: 91A05, 91A10, 91A25, 49N70, 91A60, 91A80, 91G10, 91G80

Trading algorithms that execute large orders are susceptible to exploitation by order anticipation strategies. This paper studies the influence of order anticipation strategies in a multi-investor model of optimal execution under transient price impact. Existence and uniqueness of a Nash equilibrium is established under the assumption that trading incurs quadratic transaction costs. A closedform representation of the Nash equilibrium is derived for exponential decay kernels. With this representation, it is shown that while order anticipation strategies raise the execution costs of a large order significantly, they typically do not cause price overshooting in the sense of Brunnermeier

No abstract

No abstract

No abstract