Fast and Slow Optimal Trading with Exogenous, Novermber 2022#
2. Affiliation:#
Department of Mathematics, Imperial College London
3. Keywords:#
stochastic game, high-frequency trading, institutional investor, coupled stochastic control problems, signal-adaptive strategy, Stackelberg equilibrium.
4. Url:#
5. Summary:#
(1): This article focuses on a stochastic game between a slow institutional investor and a high-frequency trader who trade on a risky asset and influence the asset’s price through their aggregated order flow, leading to the study of optimal trading strategies.
(2): The past methods in trading games assume the two players optimize their strategies separately, and do not consider the effect of their strategies on the others’ choices. The authors found that taking into account the order flow of the high-frequency trader significantly improved the institutional investor’s trading strategy. The proposed approach is well-motivated and provides a unique solution to the game by modeling two coupled stochastic control problems.
(3): The methodology involves deriving the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor, and then using the resolvent of a Fredholm integral equation to solve the institutional investor’s problem given the optimal strategy of the high-frequency trader. This leads to establishing the unique multi-period Stackelberg equilibrium of the game.
(4): The proposed methods are evaluated by showing that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the trade-off between the order flow and the trading signal. The institutional investor’s strategy is considerably more profitable when the order flow of the high-frequency trader is taken into account in her trading strategy. The achieved performance supports the goal of finding a unique Stackelberg equilibrium in the trading game.
6. Conclusion:#
(1): This article proposes a novel approach, based on coupled stochastic control problems, to study the trading game between a slow institutional investor and a high-frequency trader with exogenous factors. The article’s significance lies in its contribution to the understanding of the impact of order flow on the institutional investor’s trading strategy in a stochastic game.
(2): Innovation point: The proposed approach takes into account the order flow of the high-frequency trader, which significantly improves the institutional investor’s trading strategy. (3): Performance: The evaluated performance supports the goal of finding a unique Stackelberg equilibrium in the trading game, and the achieved results show that the institutional investor’s strategy is considerably more profitable when the order flow of the high-frequency trader is taken into account. (4): Workload: The proposed methodology involves deriving the optimal strategy of the high-frequency trader and then using the resolvent of a Fredholm integral equation to solve the institutional investor’s problem, which may require significant computational resources.
Overall, this article presents an innovative approach that addresses an important research question in the field of trading games and provides valuable insights into the effects of order flow on an institutional investor’s trading strategy. However, further research may be necessary to assess the generalizability and scalability of the proposed methodology.