标题： 具有交易成本的多资产投资与消费问题 显示英文标题

标题： A multi-asset investment and consumption problem with transaction costs

摘要： 在本文中，我们研究了一个具有比例交易成本的多资产Merton投资和消费问题。一般来说，在此类问题中很难取得解析进展，但我们将特殊情况限定为除一种我们称为不流动资产的单一资产的买卖外，其他交易成本均为零的情况。假设代理人的效用函数为CRRA形式，资产价格遵循指数布朗运动，我们证明了底层的HJB方程可以转化为一阶微分方程的边界值问题。最优策略是在总投资组合中投入该资产的比例超出固定区间时才交易不流动资产。多资产问题的重要性质（包括问题是否适定、不适定，或仅在交易成本较大时适定）可以从一个单变量的二次函数和另一个代数函数的行为中推断出来。 显示英文摘要

摘要： In this article we study a multi-asset version of the Merton investment and consumption problem with proportional transaction costs. In general it is difficult to make analytical progress towards a solution in such problems, but 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. Assuming agents have CRRA utilities and asset prices follow exponential Brownian motions we show that the underlying HJB equation can be transformed into a boundary value problem for a first order differential equation. The optimal strategy is to trade the illiquid asset only when the fraction of the total portfolio value invested in this asset falls outside a fixed interval. Important properties of the multi-asset problem (including when the problem is well-posed, ill-posed, or well-posed only for large transaction costs) can be inferred from the behaviours of a quadratic function of a single variable and another algebraic function.