Position-building in competition with real-world constraints

ArXiv ID: 2409.15459 “View on arXiv”

Authors: Unknown

Abstract

This paper extends the optimal-trading framework developed in arXiv:2409.03586v1 to compute optimal strategies with real-world constraints. The aim of the current paper, as with the previous, is to study trading in the context of multi-player non-cooperative games. While the former paper relies on methods from the calculus of variations and optimal strategies arise as the solution of partial differential equations, the current paper demonstrates that the entire framework may be re-framed as a quadratic programming problem and cast in this light constraints are readily incorporated into the calculation of optimal strategies. An added benefit is that two-trader equilibria may be calculated as the end-points of a dynamic process of traders forming repeated adjustments to each other’s strategy.

Keywords: optimal trading, quadratic programming, multi-player non-cooperative games, partial differential equations, equilibrium strategies, General Markets (Theoretical)

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is heavily theoretical, featuring advanced mathematics like variational methods, PDEs, and convex quadratic programming, but lacks any mention of code, backtests, or empirical data, focusing purely on computational methods for theoretical solutions.

  flowchart TD
    A["Research Goal:<br>Optimal Trading Strategies<br>with Real-World Constraints"] --> B["Methodology:<br>Formulate as Quadratic Programming Problem"]
    B --> C["Incorporate Constraints:<br>Order size, Liquidity, Risk"]
    C --> D["Compute Solutions:<br>Numerical Optimization"]
    D --> E["Dynamic Equilibrium:<br>Simulate Repeated Adjustments"]
    E --> F["Outcome:<br>Equilibrium Strategies &<br>Multi-Trader Interactions"]