OPTIMAL HIGH‐FREQUENCY TRADING IN A PRO RATA MICROSTRUCTURE WITH PREDICTIVE INFORMATION
研究在按比例分配的限价订单簿中，高频交易者如何选择市价单或限价单以优化交易策略，并考虑部分执行和过度交易风险，通过随机控制和动态规划求解，适用于短期利率期货等场景。
We propose a framework to study optimal trading policies in a one‐tick pro rata limit order book, as typically arises in short‐term interest rate futures contracts. The high‐frequency trader chooses to post either market orders or limit orders, which are represented, respectively, by impulse controls and regular controls. We discuss the consequences of the two main features of this microstructure: first, the limit orders are only partially executed, and therefore she has no control on the executed quantity. Second, the high‐frequency trader faces the overtrading risk, which is the risk of large variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic programming methods, and we provide the associated numerical resolution procedure and prove its convergence. We propose dimension reduction techniques in several cases of practical interest. We also detail a high‐frequency trading strategy in the case where a (predictive) directional information on the price is available. Each of the resulting strategies is illustrated by numerical tests.