Sufficiency of FFNN Policy Gradient for High-Dimensional Data-Driven Limit Order Book Modeling

Determine whether feedforward neural network-based policy gradient algorithms are sufficient to handle the high-dimensional state spaces that arise when modeling the entire limit order book in a data-driven manner for deep hedging with market impact, or whether alternative neural network architectures are required.

Background

The paper proposes a deep reinforcement learning (DRL) approach to dynamic hedging with market impact, using a feedforward neural network (FFNN) trained via a policy gradient algorithm. Market impact is modeled through simplified convex/concave cost functions Fa and Fb and exponentially decaying impact persistence processes A_t and B_t.

In the conclusion, the authors suggest extending the framework to a data-driven model of the entire limit order book (LOB). They explicitly note that such an extension would introduce high-dimensional state spaces and question whether the current FFNN-based policy gradient setup can handle this complexity or if a different neural network architecture would be necessary.

References

As further work, we could consider modeling the entire limit order book in a data-driven fashion instead of relying on simplifying dynamics \cref{dynamicsF}-\cref{dynamicsG} for market impacts. Such enhancement would require testing whether the FFNN-based policy gradient algorithms would be sufficient to treat high-dimensional state spaces required to deal with such framework, or if a different Neural Network architecture is needed.

— Deep Hedging with Market Impact  (2402.13326 - Neagu et al., 2024) in Section 'Conclusion and Further Work'