We investigate the optimal investment among the money market account, a liquid risky asset (e.g. stock index) and an illiquid risky asset (e.g. individual stock), where the two risky assets are cointegrated. The illiquid risky asset is subject to a proportional transaction cost and the portfolio of the three assets faces certain position limits. We develop the optimal investment strategy to maximize the gain function, which is realized through an expected sum of discounted utilities given transaction costs and position limits. The problem formulation uses a singular control framework with cointegration that determines optimal trading boundaries among holding, selling and no-trading regions. We conduct comprehensive numerical analysis on the optimal investment strategy and features of the optimal trading boundaries given various levels of position limits.

中文翻译：

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流动性和头寸限制配对交易

我们研究了货币市场账户，流动性高风险资产（例如，股票指数）和流动性低风险资产（例如，单个股票）之间的最优投资，其中两种风险资产是协整的。流动性低的风险资产要按比例支付交易费用，并且这三项资产的投资组合面临一定的头寸限制。我们开发最佳投资策略以最大化收益函数，这是通过在给定交易成本和头寸限制的情况下，通过折价公用事业的预期总和来实现的。问题表述使用具有协整关系的奇异控制框架，该框架确定了持有，出售和无交易区域之间的最佳交易边界。