We discuss the turnpike property for optimal investment and consumption problems. We find there exists a threshold value that determines the turnpike property for investment policy. The threshold value only depends on the Sharpe ratio, the riskless interest rate and the discount rate. We show that if utilities behave asymptotically like power utilities and satisfy some simple relations with the threshold value, then the turnpike property for investment holds. There is in general no turnpike property for consumption policy. We also provide the rate of convergence and illustrate the main results with examples of power and non-HARA utilities and numerical tests.

中文翻译：

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投资和消费模型的收费公路属性和收敛速度

我们讨论收费公路物业的最佳投资和消费问题。我们发现存在一个阈值，该阈值确定了投资政策的收费公路资产。阈值仅取决于夏普比率，无风险利率和折现率。我们证明，如果公用事业像电力公用事业那样渐近地表现，并且满足一些与阈值的简单关系，那么投资的收费抵押财产就成立了。消费政策通常没有收费标准。我们还提供收敛速度，并通过幂和非HARA实用程序以及数值测试的示例说明主要结果。