This study investigates the optimal execution strategy of market-making for market and limit order arrival dynamics under a novel framework that includes a synchronised factor between buy and sell order arrivals. Using statistical tests, we empirically confirm that a synchrony propensity appears in the market, where a buy order arrival tends to follow the sell order’s long-term mean level and vice versa. This is presumably closely related to the drastic increase in the influence of high-frequency trading activities in markets. To solve the high-dimensional Hamilton–Jacobi–Bellman equation, we propose a deep neural network approximation and theoretically verify the existence of a network structure that guarantees a sufficiently small loss function. Finally, we implement the terminal profit and loss profile of market-making using the estimated optimal strategy and compare its performance distribution with that of other feasible strategies. We find that our estimation of the optimal market-making placement allows significantly stable and steady profit accumulation over time through the implementation of strict inventory management.

这项研究调查了在一个新颖的框架下市场做市和限制订单到达动态的最优执行策略，该框架包括买卖订单到达之间的同步因素。通过统计检验，我们凭经验确认了市场中出现了同步倾向，在该市场中，买单到达往往遵循卖单的长期平均水平，反之亦然。据推测，这与高频交易活动在市场上的影响力的急剧增加密切相关。为了解决高维Hamilton–Jacobi–Bellman方程，我们提出了一个深度神经网络逼近，并从理论上验证了保证足够小的损失函数的网络结构的存在。最后，我们使用估计的最佳策略来实现做市的终端盈亏状况，并将其绩效分配与其他可行策略进行比较。我们发现，通过执行严格的库存管理，我们对最佳做市商位置的估计可以使随着时间的推移显着稳定和稳定的利润积累。