In this article, we study a multi-asset version of the Merton investment and consumption problem with CRRA utility and proportional transaction costs. We specialise to a case where transaction costs are zero except for sales and purchases of a single asset which we call the illiquid asset. We show that the underlying HJB equation can be transformed into a boundary value problem for a first order differential equation. Important properties of the multi-asset problem (including when the problem is well-posed, ill-posed, or well-posed for some values of transaction costs only) can be inferred from the behaviours of a quadratic function of a single variable and another algebraic function.

中文翻译：

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带有交易成本的多资产投资和消费问题

在本文中，我们研究了带有CRRA效用和成比例交易成本的默顿投资和消费问题的多资产版本。我们专门研究交易成本为零的情况，但买卖单个资产（我们称为非流动性资产）除外。我们表明，基本的HJB方程可以转化为一阶微分方程的边值问题。可以从单个变量和另一个变量的二次函数的行为中推断出多资产问题的重要属性（包括仅在某些交易成本值的情况下是适度的，不适度的或适度的）。代数函数。