Portfolio Optimization Applications of Stochastic Receding Horizon Control
Portfolio Optimization Applications of Stochastic Receding Horizon Control
复制标题
随机后退水平控制的投资组合优化应用
DOI：
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发表时间：
2007
期刊：
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通讯作者：
J. Primbs
中科院分区：
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作者：
J. Primbs
针对有约束的动态投资组合优化问题，提出了随机滚动时域控制方法。特别是，我们制定了两个投资组合优化问题。第一个问题是风险调整后的财富最大化问题，第二个问题是最优跟踪股票指数的问题。我们认为这两个问题的概率机会约束。通过将问题中的动态建模为线性系统受状态和控制乘性噪声的影响，并用二次期望约束近似线性机会约束，我们证明了两者都可以用随机滚动时域控制来逼近。特别是，我们使用一个闭环版本的随机滚动时域控制的在线优化解决作为一个半定规划。数值算例表明，随机滚动时域控制是求解约束投资组合优化问题的一种新方法。
This paper develops stochastic receding horizon control for constrained dynamic portfolio optimization problems. In particular, we formulate two portfolio optimization problems. The first is that of risk adjusted wealth maximization, while the second is the problem of optimally tracking an index of stocks with fewer stocks. We consider both of these problems subject to probabilistic chance constraints. By modeling the dynamics in the problems as linear systems subject to state and control multiplicative noise, and approximating linear chance constraints with quadratic expectation constraints, we show that both can be approached using stochastic receding horizon control. In particular, we use a closed loop version of stochastic receding horizon control where the on-line optimization is solved as a semi-definite program. Numerical examples demonstrate the computations involved in these problems and indicate that stochastic receding horizon control is a promising new approach to constrained portfolio optimization problems.