Multi-period mean-variance portfolio selection with regime switching and a stochastic cash flow

► A non-self-financing portfolio optimization problem is investigated. ► Returns of assets and the cash flow depend on the states of a stochastic market. ► Several examples are given to explain the stochastic cash flow in the real life. ► Closed-form expressions of the optimal strategy and efficient frontier are derived. ► Numerical examples are given to demonstrate the effect of the cash flow.