Continuous-Time Portfolio Optimization for Absolute Return Funds
Continuous-Time Portfolio Optimization for Absolute Return Funds
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DOI：
10.1007/s10690-022-09365-9
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发表时间：
2021-08
影响因子：
1.7
通讯作者：
Masashi Ieda
中科院分区：
文献类型：
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作者：
Masashi Ieda
本文研究了一个具有以下特征的连续时间投资组合优化问题：（i）无卖空约束;（ii）杠杆约束，即投资组合权重之和的上限;以及（iii）基于投资者财富与预定目标财富水平之间的较低均方误差的性能准则。由于目标水平是由一个独立于市场指数的确定性函数定义的，它对应于绝对回报基金的标准。该模型是制定使用显式边界条件的随机控制框架。相应的Hamilton-Jacobi-Bellman方程的数值求解使用基于核的配置方法。然而，一个简单的实现并不提供一个稳定的和可接受的投资策略，因此，提出了一些技术来解决这个缺点。通过应用所提出的方法，得到两个数值结果：一个使用人工数据，另一个使用日本组织的经验数据。第一个结果有两个含义：如何稳定的数值解，和一种技术，以规避接近终端时间的验证成功率。第二个结果表明，在本文讨论的背景下，杠杆是不可避免的，以实现目标水平。
This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a performance criterion based on the lower mean square error between the investor’s wealth and a predetermined target wealth level. Since the target level is defined by a deterministic function independent of market indices, it corresponds to the criterion of absolute return funds. The model is formulated using the stochastic control framework with explicit boundary conditions. The corresponding Hamilton–Jacobi–Bellman equation is solved numerically using the kernel-based collocation method. However, a straightforward implementation does not offer a stable and acceptable investment strategy; thus, some techniques to address this shortcoming are proposed. By applying the proposed methodology, two numerical results are obtained: one uses artificial data, and the other uses empirical data from Japanese organizations. There are two implications from the first result: how to stabilize the numerical solution, and a technique to circumvent the plummeting achievement rate close to the terminal time. The second result implies that leverage is inevitable to achieve the target level in the setting discussed in this paper.