Optimal posting price of limit orders: learning by trading

TL;DR

This paper introduces a learning algorithm for traders to optimize their limit order posting prices, ensuring convergence and cost minimization through theoretical proofs and practical criteria, validated by simulations and real market data.

Contribution

It proposes a novel iterative procedure for optimal limit order pricing with proven convergence and practical guidelines for implementation.

Findings

Algorithm converges almost surely under certain conditions.

Practical criteria ensure the algorithm's applicability.

Numerical experiments validate the approach on simulated and real data.

Abstract

Considering that a trader or a trading algorithm interacting with markets during continuous auctions can be modeled by an iterating procedure adjusting the price at which he posts orders at a given rhythm, this paper proposes a procedure minimizing his costs. We prove the a.s. convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameters to ensure that the conditions to use the algorithm are fulfilled (using notably the co-monotony principle). We illustrate our results with numerical experiments on both simulated data and using a financial market dataset.