Solving Optimal Execution Problems via In-Context Operator Networks

TL;DR

This paper introduces ICON-OCnet, a transformer-based neural network architecture that learns and infers unknown price impact models from limited data to optimize order execution strategies in financial markets.

Contribution

The paper presents a novel in-context operator learning framework combining offline pre-training and online inference for optimal execution in unknown price impact environments.

Findings

ICON accurately infers unseen propagator kernels from data prompts.

ICON-OCnet retrieves the exact optimal execution strategy in tested models.

The approach generalizes to path-dependent stochastic control problems.

Abstract

We propose a novel transformer-based neural network architecture (ICON-OCnet) for solving optimal order execution problems in the presence of unknown price impact. Our architecture facilitates data-driven in-context operator learning for the incurred price impact by merging offline pre-training with online few-shot prompting inference. First, the operator learning component (ICON) learns the prevailing price impact environment from only a few executed trade and price impact trajectories (time series data) provided as context. Second, we employ ICON as a surrogate operator to train a neural network policy (OCnet) for the optimal order execution strategy for the price impact regime inferred from the in-context examples. We study the efficiency of our approach for linear propagator models with path-dependent transient price impact and explicitly known optimal execution strategies. In this model class, price impact persists and decays over time according to some propagator kernel. We illustrate that ICON is capable of accurately inferring the underlying price impact model from the data prompts, even for propagator kernels not seen in the training data. Moreover, we demonstrate that ICON-OCnet correctly retrieves the exact optimal order execution strategy for the model generating the in-context examples. Our introduced methodology is very general, offering a new approach to solving path-dependent optimal stochastic control problems sample-based with unknown state dynamics.