论文标题
带有棘轮资本基准的最佳跟踪作品集
Optimal Tracking Portfolio with A Ratcheting Capital Benchmark
论文作者
论文摘要
本文通过最佳跟踪棘轮基准基准过程来研究有限的地平线投资组合管理。假定基金经理可以动态地注入资本到投资组合帐户中，以便总资本在每个中间时间占主导地位的基准平台过程。提出的跟踪问题是为了最大程度地减少累积资本注入成本。我们首先将原始问题与地板约束转变为无约束的控制问题，但是，在运行最大成本下。通过识别具有反射的受控状态过程，该问题进一步证明是等同于辅助问题，这导致具有Neumann边界条件的非线性汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程。通过采用双重变换，概率表示和一些随机流分析，可以建立独特的经典解决方案。仔细证明了验证定理，从而给出了反馈最佳投资组合的完整表征。当索引过程通过几何布朗尼运动建模时，还讨论了市场指数跟踪的应用。
This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total capital dominates a non-decreasing benchmark floor process at each intermediate time. The tracking problem is formulated to minimize the cost of accumulated capital injection. We first transform the original problem with floor constraints into an unconstrained control problem, however, under a running maximum cost. By identifying a controlled state process with reflection, the problem is further shown to be equivalent to an auxiliary problem, which leads to a nonlinear Hamilton-Jacobi-Bellman (HJB) equation with a Neumann boundary condition. By employing the dual transform, the probabilistic representation and some stochastic flow analysis, the existence of the unique classical solution to the HJB equation is established. The verification theorem is carefully proved, which gives the complete characterization of the feedback optimal portfolio. The application to market index tracking is also discussed when the index process is modeled by a geometric Brownian motion.
