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.

翻译：本文扩展了arXiv:2409.03586v1中开发的最优交易框架，以计算包含现实约束的最优策略。与先前研究一致，本文旨在研究多人非合作博弈背景下的交易行为。前文主要依赖变分法，其最优策略表现为偏微分方程的解；而本文证明整个框架可重构为二次规划问题，在此视角下各类约束条件能自然融入最优策略的计算过程。一个额外优势是：双交易者均衡可被计算为动态过程的终点，该过程描述了交易者根据对方策略进行重复调整的交互机制。