论文标题
限制了随机LQ控制，并使用制度切换并应用于投资组合选择
Constrained stochastic LQ control with regime switching and application to portfolio selection
论文作者
论文摘要
本文涉及随机线性季度最佳控制问题，其制度切换，随机系数和锥体控制约束。系数的随机性来自两个方面：布朗运动和马尔可夫链。使用ITô的引理将其用于马尔可夫链，我们通过两个新的随机Riccati方程（ESRE）明确获得最佳状态反馈控制和最佳成本值。我们使用工具（包括多维比较定理，截断功能技术，日志转换和John-Nirenberg的不平等现象）证明了两种ESRE的存在和唯一性。然后将这些结果应用于研究均值变化的投资组合选择问题，有或没有卖空禁令，并取决于布朗运动和马尔可夫链，并随机参数。最后，有效的投资组合和有效的边界以封闭形式呈现。
This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients, and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and the Markov chain. Using Itô's lemma for Markov chain, we obtain the optimal state feedback control and optimal cost value explicitly via two new systems of extended stochastic Riccati equations (ESREs). We prove the existence and uniqueness of the two ESREs using tools including multidimensional comparison theorem, truncation function technique, log transformation and the John-Nirenberg inequality. These results are then applied to study mean-variance portfolio selection problems with and without short-selling prohibition with random parameters depending on both the Brownian motion and the Markov chain. Finally, the efficient portfolios and efficient frontiers are presented in closed forms.
