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We consider a model in which a trader aims to maximize expected risk-adjusted profit while trading a single security. In our model, each price change is a linear combination of observed factors, impact resulting from the traders current and prior activity, and unpredictable random effects. The trader must learn coefficients of a price impact model while trading. We propose a new method for simultaneous execution and learning - the confidence-triggered regularized adaptive certainty equivalent (CTRACE) policy - and establish a poly-logarithmic finite-time expected regret bound. This bound implies that CTRACE is efficient in the sense that the ({epsilon},{delta})-convergence time is bounded by a polynomial function of 1/{epsilon} and log(1/{delta}) with high probability. In addition, we demonstrate via Monte Carlo simulation that CTRACE outperforms the certainty equivalent policy and a recently proposed reinforcement learning algorithm that is designed to explore efficiently in linear-quadratic control problems.
Executing a basket of co-integrated assets is an important task facing investors. Here, we show how to do this accounting for the informational advantage gained from assets within and outside the basket, as well as for the permanent price impact of m
In light of micro-scale inefficiencies induced by the high degree of fragmentation of the Bitcoin trading landscape, we utilize a granular data set comprised of orderbook and trades data from the most liquid Bitcoin markets, in order to understand th
We analyze a proprietary dataset of trades by a single asset manager, comparing their price impact with that of the trades of the rest of the market. In the context of a linear propagator model we find no significant difference between the two, sugge
We revisit the epsilon-intelligence model of Toth et al.(2011), that was proposed as a minimal framework to understand the square-root dependence of the impact of meta-orders on volume in financial markets. The basic idea is that most of the daily li
We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the