Optimal Internalization of Toxic Order Flow with Partial Information

Summary

The paper models a central trading desk that receives client orders with hidden, persistent directional toxicity. The desk must decide whether to internalize incoming flow or externalize it to the market. Externalization incurs price impact and can trigger additional market feedback. The objective is to maximize daily trading P&L while penalizing inventory remaining at the end of the day.

The authors formulate the problem as partially observable stochastic control. They first derive filtered dynamics for inventory and toxicity using the desk’s observable information, converting the task into a fully observed control problem. A variational method then yields a unique optimal trading strategy. The paper illustrates the framework under both momentum and mean-reverting toxicity scenarios. The document describes model-based analysis, but provides no numerical performance figures or evidence from live trading; practical results would depend on the model assumptions and available observations.

Key ideas

• The desk chooses between internalizing client orders and externalizing them to the market.
• Externalized flow creates price impact costs and market feedback.
• The objective combines daily trading P&L with a penalty for end-of-day inventory.
• Filtering hidden inventory and toxicity dynamics converts the partially observed problem into a fully observed control problem.
• A variational approach derives a unique strategy, illustrated for momentum and mean-reverting toxicity.

Tags

# Unwinding Toxic Flow with Partial Information


# Unwinding Toxic Flow with Partial Information









We consider a central trading desk which aggregates the inflow of clients' orders with unobserved toxicity, i.e. persistent adverse directionality. The desk chooses either to internalise the inflow or externalise it to the market in a cost-effective manner. In this model, externalising the order flow creates both price impact costs and an additional market feedback reaction for the inflow of trades. The desk's objective is to maximise the daily trading P&L subject to end-of-day inventory penalisation. We formulate this setting as a partially observable stochastic control problem and solve it in two steps. First, we derive the filtered dynamics of the inventory and toxicity, projected to the observed filtration, which turns the stochastic control problem into a fully observed problem. Then we use a variational approach in order to derive the unique optimal trading strategy. We illustrate our results for various scenarios in which the desk faces momentum and mean-reverting toxicity.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.