Adding Machine Learning Signals to Stochastic Trading Control
Summary
The discussion explains that a machine learning alpha signal can enter a stochastic control problem if it is given a temporal model that supports planning. One simple approach is to represent known time variation in trading opportunities and incorporate it into an Almgren–Chriss style mean-variance execution optimizer. A richer approach models signals as Ornstein–Uhlenbeck processes with distinct time scales, as explored in cited research on optimal trading with signals.
The central caveat is that this modeling task is difficult: a predictive signal alone does not specify how it evolves over time, which a control policy needs. Trading may also change the signals through market impact, so a realistic formulation may need a closed-loop model of both signal dynamics and the trader’s actions. The document offers conceptual direction and literature references, but no empirical comparison or implementation details.
Key ideas
- Stochastic control requires a temporal structure for signals to support planning.
- Known time patterns in trading opportunities can be incorporated into mean-variance execution optimization.
- Ornstein–Uhlenbeck processes with different time scales offer one way to model signal evolution.
- A trader’s market impact can influence the signals being traded, creating a closed-loop modeling problem.
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# How to merge ML-based $\alpha$-signal with stochastic control approach?
# How to merge ML-based $\alpha$-signal with stochastic control approach?
I'm having a hypothetical situation where I have a set of ML-based alpha signals $\{\alpha_i\}_{i=1}^{N}$ that describe a different states of order book - imbalances, order flow, spread properties etc. I wonder, what is the correct approach to merge those signals with stochastic control approach to generate a decision-making process.
Most of the papers I saw about (for example this one) deal with alpha signals in context of stochastic processes. How does one proceed in the case where $\alpha$ is given by ML model and not a stochastic process?
## Answer by lehalle (score 1)
https://quant.stackexchange.com/a/77828
A first answer is explained in Market microstructure knowledge needed for controlling an intra-day trading process that is Chapter 21 of Fouque, Jean-Pierre, and Joseph A. Langsam, eds. Handbook on systemic risk. Cambridge University Press, 2013.
If you know some characteristics of your arbitrage opportunities as a function of time (for instance that you have usually more opportunities after the opening than around 2pm), you can tell that to your optimiser. This chapter tells you how to include them in an Almgren-Chriss (ie mean-variance) like optimisation scheme:
Another (and more generic) way to answer to your question is to explain that stochastic control is about planning; to plan you need to have a temporal structure. The simplest one is the one used in the chapter mentioned earlier. You can have more structure, for instance to formulate your signal(s) as Ornstein-Uhlenbeck processes with different time scales. It is done in C-A L and Eyal Neuman. "Incorporating signals into optimal trading" Finance and Stochastics 23 (2019): 275-311. You will see that it is not easy... The worst is that usually when you trade your signal you influence them, hence you should model a closed loop between the signal and your own impact.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.