2020/04/24 by Ying Hu, Hu, Ying, Xiaomin Shi +3 · 5 citations
Decision Sciences · Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2004.11832
openalex publication_date 2020/04/24 · openalex created_date 2021/09/27 · openalex updated_date 2026/07/28
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.