Paper: arXiv 2601.03215

Authors: Youssef Ouazzani Chahdi, Nathan De Carvalho, Grégoire Szymanski

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.

Complexity vs Empirical Score

  • Math Complexity: 9.2/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is dense with advanced mathematics, featuring nonlinear stochastic Fredholm equations, coercivity, and weak lower semicontinuity proofs, while empirical validation is limited to conceptual numerical experiments without data, code, or backtest-ready implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Find optimal trading strategy<br>under market resistance"] --> B["Model Formulation<br>Concave transient impact &<br>endogenous resistance via fixed-point"]
  B --> C["Key Methodology<br>Derive nonlinear stochastic<br>Fredholm equation (optimality)"]
  C --> D{"Resistance Function?"}
  D --> E["Linear Case"]
  D --> F["Strictly Convex Case"]
  E --> G["Existence &<br>Uniqueness Proof"]
  F --> H["Existence Proof via<br>Coercivity & WLSC"]
  G --> I["Iterative Scheme<br>Exponential convergence"]
  H --> I
  I --> J["Computational Process<br>Numerical experiments<br>Round-trip strategies"]
  J --> K["Key Outcomes<br>Validated optimal control &<br>convergence rate"]

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8 of 520 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.