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This paper is devoted to study the effects arising from imposing a Value-at-Risk (VaR) constraint in mean-variance portfolio selection problem for an investor who receives a stochastic cash flow which he/she must then invest in a continuous-time financial market. For simplicity, the authors assume that there is only one investment opportunity available for the investor, a risky stock. Using techniques of stochastic Linear-Quadratic (LQ) control, the optimal mean-variance investment strategy with and without VaR constraint are de-rived explicitly in closed forms, based on solution of corresponding Hamilton-Jacobi-Bellman (HJB) equation. Furthermore, some numerical examples are proposed to show how the addition of the VaR constraint affects the optimal strategy.
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