We study the problem of dynamically trading multiple futures contracts with different underlying assets. To capture the joint dynamics of stochastic bases for all traded futures, we propose a new model involving a multi-dimensional scaled Brownian bridge that is stopped before price convergence. This leads to the analysis of the corresponding Hamilton–Jacobi–Bellman equations, whose solutions are derived in semi-explicit form. The resulting optimal trading strategy is a long-short policy that accounts for whether the futures are in contango or backwardation. Our model also allows us to quantify and compare the values of trading in the futures markets when the underlying assets are traded or not. Numerical examples are provided to illustrate the optimal strategies and the effects of model parameters.

中文翻译：

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一篮子期货合约的最佳交易

我们研究了动态交易具有不同基础资产的多个期货合约的问题。为了捕获所有交易期货的随机基础的联合动态，我们提出了一个新模型，其中涉及一个多维比例的布朗桥，该桥在价格趋同之前就已停止。这导致对相应的Hamilton–Jacobi–Bellman方程的分析，其解以半显式形式导出。最终的最佳交易策略是多空策略，该策略说明了期货是处于期货交易还是现货交易。我们的模型还允许我们量化和比较基础资产是否交易的期货市场交易价值。数值例子说明了最优策略和模型参数的影响。