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Based on the mean-variance portfolio selection under multi-period criterion, this paper focuses on the study of the uncertain time horizon and the regime-switching market including the bankruptcy state, where the conditional distribution of exit time is followed by the market state. When the market enters the bankruptcy state, investors are assumed to get back δ part of the wealth from the bankrupt company, where δ refers to the retrieval rate. By introducing the Lagrange multiplier λ , wedoi:10.4236/jmf.2019.92008 fatcat:qgejl6nnbzc6hno5ajemudtzwi