Optimal Liquidation of Child Limit Orders
研究了基于订单簿短期动量指标的子订单最优放置问题，构建最优多重停时模型，发现最优策略由动量指标首次穿越时变边界决定，且策略激进程度随买卖价差减小、动量影响增大或剩余时间缩短而增强。
The present paper studies the optimal placement problem of a child order. In practice, short-term momentum indicators inferred from order book data play important roles in order placement decisions. In the present work, we first propose to explicitly model the short-term momentum indicator and then formulate the order placement problem as an optimal multiple stopping problem. In contrast to the common formulation in the existing literature, we allow zero refracting period between consecutive stopping times to take into account the common practice of submitting multiple orders at the same time. This optimal multiple stopping problem will be explored over both infinite and finite horizons. It is shown that the optimal placement of a child order and the optimal replacement of outstanding limit orders by market ones are determined by first passage times of the short-term momentum indicator across a sequence of time-dependent boundaries. The aggressiveness of the optimal order replacement strategy is also examined via several numerical examples. In particular, our work illustrates that the optimal order replacement strategy is more aggressive when the bid–ask spread is smaller, when the impact from the momentum indicator is larger, or when the remaining time becomes shorter. All of these decision-making behaviors predicted by our model are natural and agree with empirical studies in the existing literature.