论文标题
动态和静态基金分离及其长期最佳投资的稳定性
Dynamic and static fund separations and their stability for long-term optimal investments
论文作者
论文摘要
本文研究了动态和静态基金分离及其在三个模型类别下长期最佳投资的稳定性。投资者在不完整的市场下，通过安全资产，几个风险资产和单个状态变量组成的不完整市场，最大化预期的效用。两个模型类中的状态变量分别遵循3/2过程和逆Bessel过程。另一个市场模型具有部分观察到的状态变量，该变量模型为Ornstein-Uhlenbeck状态过程。我们表明，该实用程序最大化的动态最佳投资组合由M+3投资组合组成：安全资产，近视投资组合，M时间独立的投资组合和周期投资组合。随着时间的流逝，跨期投资组合最终消失了，导致动态投资组合收敛到M+2个投资组合，称为静态投资组合。我们还证明，在模型参数扰动下，收敛是稳定的。另外，从长远来看，跨期投资组合对小参数的敏感性也消失了。针对介绍的模型明确计算了跨期投资组合及其灵敏度的收敛速率。
This paper investigates dynamic and static fund separations and their stability for long-term optimal investments under three model classes. An investor maximizes the expected utility with constant relative risk aversion under an incomplete market consisting of a safe asset, several risky assets, and a single state variable. The state variables in two of the model classes follow a 3/2 process and an inverse Bessel process, respectively. The other market model has the partially observed state variable modeled as an Ornstein-Uhlenbeck state process. We show that the dynamic optimal portfolio of this utility maximization consists of m+3 portfolios: the safe asset, the myopic portfolio, the m time-independent portfolios, and the intertemporal portfolio. Over time, the intertemporal portfolio eventually vanishes, leading the dynamic portfolio to converge to m+2 portfolios, referred to as the static portfolio. We also prove that the convergence is stable under model parameter perturbations. In addition, sensitivities of the intertemporal portfolio with respect to small parameters perturbations also vanish in the long run. The convergence rate for the intertemporal portfolio and its sensitivities are computed explicitly for the presented models.
