英文标题：
《Portfolio Optimization with Delay Factor Models》
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作者：
Shuenn-Jyi Sheu, Li-Hsien Sun, Zheng Zhang
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最新提交年份：
2018
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英文摘要：
We propose an optimal portfolio problem in the incomplete market where the underlying assets depend on economic factors with delayed effects, such models can describe the short term forecasting and the interaction with time lag among different financial markets. The delay phenomenon can be recognized as the integral type and the pointwise type. The optimal strategy is identified through maximizing the power utility. Due to the delay leading to the non-Markovian structure, the conventional Hamilton-Jacobi-Bellman (HJB) approach is no longer applicable. By using the stochastic maximum principle, we argue that the optimal strategy can be characterized by the solutions of a decoupled quadratic forward-backward stochastic differential equations(QFBSDEs). The optimality is verified via the super-martingale argument. The existence and uniqueness of the solution to the QFBSDEs are established. In addition, if the market is complete, we also provide a martingale based method to solve our portfolio optimization problem, and investigate its connection with the proposed FBSDE approach. Finally, two particular cases are analyzed where the corresponding FBSDEs can be solved explicitly.
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中文摘要：
在标的资产依赖于具有时滞效应的经济因素的不完全市场中，我们提出了一个最优投资组合问题，该模型可以描述不同金融市场之间的短期预测和时滞相互作用。延迟现象可分为积分型和逐点型。通过最大化电力利用率来确定最优策略。由于延迟导致非马尔可夫结构，传统的Hamilton-Jacobi-Bellman（HJB）方法不再适用。利用随机极大值原理，我们证明了最优策略可以用一个解耦的二次正倒向随机微分方程（QFBSDEs）的解来描述。通过超鞅参数验证了该算法的最优性。建立了QFBSDEs解的存在唯一性。此外，如果市场是完全的，我们还提供了一种基于鞅的方法来解决我们的投资组合优化问题，并研究其与所提出的FBSDE方法的联系。最后，分析了可以显式求解相应FBSDE的两种特殊情况。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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