Trading with market resistance and concave price impact

TL;DR

This paper develops a model for optimal trading that accounts for endogenous market resistance and price overreactions, deriving equations for optimal strategies and proposing an iterative solution method validated by numerical experiments.

Contribution

It introduces a novel market impact model with endogenous resistance, deriving a nonlinear Fredholm equation for optimal strategies and providing an iterative solution approach.

Findings

Existence and uniqueness of optimal strategies under linear resistance.

An iterative scheme converging exponentially to the solution.

Numerical experiments illustrating strategies under various resistance profiles.

Abstract

We consider an optimal trading problem under a market impact model with endogenous market resistance generated by a sophisticated trader who (partially) detects metaorders and trades against them to exploit price overreactions induced by the order flow. The model features a concave transient impact driven by a power-law propagator with a resistance term responding to the trader's rate via a fixed-point equation involving a general resistance function. We derive a (non)linear stochastic Fredholm equation as the first-order optimality condition satisfied by optimal trading strategies. Existence and uniqueness of the optimal control are established when the resistance function is linear, and an existence result is obtained when it is strictly convex using coercivity and weak lower semicontinuity of the associated profit-and-loss functional. We also propose an iterative scheme to solve the nonlinear stochastic Fredholm equation and prove an exponential convergence rate. Numerical experiments confirm this behavior and illustrate optimal round-trip strategies under "buy" signals with various decay profiles and different market resistance specifications.