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Constrained stochastic LQ control with regime switching and application to portfolio selection

Abstract 

We study 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 Ito'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 BMO martingale. 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. Based on a joint work with Ying Hu and Zuo Quan Xu. 


报告人简介:时晓敏,山东财经大学数学与数量经济学院副教授,2017 年毕业于山东大学金融数学与金融工程专业,研究兴趣为随机控制及其在金融数学中的应用。在Ann. Appl. Probab., Systems Control Letters, Math. Control Relat. Fields 等期刊发表多篇论文。