A multi-asset investment and consumption problem with transaction costs
研究了多资产版本的Merton投资消费问题，考虑比例交易成本，将HJB方程转化为一阶微分方程边值问题，分析了问题适定性的条件。
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.