Optimal trading without optimal control

TL;DR

This paper proposes a heuristic for optimal trading in limit-order-book markets using the gradient of the Bellman value function as a microstructure alpha, bridging optimal control and practical trading strategies.

Contribution

It introduces a novel heuristic linking value function gradients to trading signals, enabling near-optimal trading without explicit control solutions.

Findings

Heuristic aligns with long-term optimal behavior in trading.

Applicable to a wide range of utility-maximization problems.

Provides a practical method for trading in limit-order markets.

Abstract

A hypothetical risk-neutral agent who trades to maximize the expected profit of the next trade will approximately exhibit long-term optimal behavior as long as this agent uses the vector $p = \nabla V (t, x)$ as effective microstructure alphas, where V is the Bellman value function for a smooth relaxation of the problem. Effective microstructure alphas are the steepest-ascent direction of V , equal to the generalized momenta in a dual Hamiltonian formulation. This simple heuristics has wide-ranging practical implications; indeed, most utility-maximization problems that require implementation via discrete limit-order-book markets can be treated by our method.