{"ID":2890101,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.19824","arxiv_id":"2507.19824","title":"Optimal mean-variance portfolio selection under regime-switching-induced stock price shocks","abstract":"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 $\\ell$-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 $2\\ell$-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.","short_abstract":"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, b...","url_abs":"https://arxiv.org/abs/2507.19824","url_pdf":"https://arxiv.org/pdf/2507.19824v1","authors":"[\"Xiaomin Shi\",\"Zuo Quan Xu\"]","published":"2025-07-26T06:48:11Z","proceeding":"q-fin.PM","tasks":"[\"q-fin.PM\",\"math.OC\",\"math.PR\",\"q-fin.MF\"]","methods":"[]","has_code":false}