2025/07/26 by Xiaomin Shi, Shi, Xiaomin, Zuo Quan Xu +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2507.19824
openalex publication_date 2025/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate mean-variance (MV) portfolio selection problems with jumps in a regime-switching financial model. The novelty of our approach lies in allowing not only the market parameters -- such as the interest rate, appreciation rate, volatility, and jump intensity -- to depend on the market regime, but also in permitting stock prices to experience jumps when the market regime switches, in addition to the usual micro-level jumps. This modeling choice is motivated by empirical observations that stock prices often exhibit sharp declines when the market shifts from a ``bullish'' to a ``bearish'' regime, and vice versa. By employing the completion-of-squares technique, we derive the optimal portfolio strategy and the efficient frontier, both of which are characterized by three systems of multi-dimensional ordinary differential equations (ODEs). Among these, two systems are linear, while the first one is an ℓ-dimensional, fully coupled, and highly nonlinear Riccati equation. In the absence of regime-switching-induced stock price shocks, these systems reduce to simple linear ODEs. Thus, the introduction of regime-switching-induced stock price shocks adds significant complexity and challenges to our model. Additionally, we explore the MV problem under a no-shorting constraint. In this case, the corresponding Riccati equation becomes a 2ℓ-dimensional, fully coupled, nonlinear ODE, for which we establish solvability. The solution is then used to explicitly express the optimal portfolio and the efficient frontier.