In this paper, we investigate an investment–consumption optimization problem in continuous-time settings, where the expected rate of return from a risky asset is predictable with an observable factor and an unobservable factor. Based on observable information, a decision-maker learns about the unobservable factor while making investment–consumption decisions. Both factors are supposed to follow a mean-reverting process. Also, we relax the assumption for perfect liquidity of the risky asset through incorporating proportional transaction costs that are incurred in trading the risky asset. In such way, a form of friction posing liquidity risk to the investor is examined. Dynamic programming principle coupled with an Hamilton–Jacobi–Bellman (HJB) equation are adopted to discuss the problem. Applying an asymptotic method with small transaction costs being taken as a perturbation parameter, we determine the frictional value function by solving the first and second corrector equations. For the numerical implementation of the proposed approach, a Monte-Carlo-simulation-based approximation algorithm is adopted to solve the second corrector equation. Finally, numerical examples and their economic interpretations are discussed.

中文翻译：

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通过交易成本优化投资-消费并了解回报可预测性


在本文中，我们研究了连续时间设置中的投资-消费优化问题，其中风险资产的预期回报率可以通过可观察因素和不可观察因素进行预测。基于可观察的信息，决策者在做出投资消费决策时了解不可观察的因素。这两个因素都应该遵循均值回归过程。此外，我们通过纳入风险资产交易中产生的比例交易成本，放宽了风险资产完美流动性的假设。通过这种方式，可以检查对投资者造成流动性风险的摩擦形式。采用动态规划原理结合 Hamilton-Jacobi-Bellman (HJB) 方程来讨论该问题。采用渐进方法，以较小的交易成本作为扰动参数，通过求解第一和第二校正方程来确定摩擦值函数。为了数值实现所提出的方法，采用基于蒙特卡罗模拟的近似算法来求解第二个校正方程。最后，讨论了数值例子及其经济解释。