Paper: arXiv 2503.02496

Abstract

This paper addresses the trade-off between internalisation and externalisation in the management of stochastic trade flows. We consider agents who must absorb flows and manage risk by deciding whether to warehouse it or hedge in the market, thereby incurring transaction costs and market impact. Unlike market makers, these agents cannot skew their quotes to attract offsetting flows and deter risk-increasing ones, leading to a fundamentally different problem. Within the Almgren-Chriss framework, we derive almost-closed-form solutions in the case of quadratic execution costs, while more general cases require numerical methods. In particular, we discuss the challenges posed by artificial boundary conditions when using classical grid-based numerical PDE techniques and propose reinforcement learning methods as an alternative.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper involves advanced stochastic optimal control, HJB equations, and Riccati differential equations, placing it in the high math complexity range. However, it lacks empirical backtests or real-world data implementation, focusing instead on theoretical models and proposing reinforcement learning as an alternative to numerical methods, resulting in low empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Optimal Stochastic<br>Trade Flow Management"] --> B["Methodology:<br>Almgren-Chriss Framework<br>+ Reinforcement Learning"]
  B --> C["Inputs & Constraints:<br>Stochastic Flows, Quadratic<br>Costs, No Quote Skewing"]
  C --> D{"Computational Process"}
  D --> E["Analytical Solution:<br>Quadratic Costs"]
  D --> F["Numerical PDE:<br>Artificial Boundary Challenges"]
  D --> G["RL Approach:<br>Bypasses Grid Limitations"]
  E --> H["Key Findings & Outcomes"]
  F --> H
  G --> H
  H --> I["Pareto-optimal<br>Risk-Cost Trade-offs"]
  H --> J["RL Effectiveness for<br>Complex/Multidimensional Cases"]
  H --> K["Generalized Framework<br>beyond Market Making"]