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Optimal mean-variance investment strategy under value-at-risk constraints

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  • Jun Ye
  • Tiantian Li
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    Abstract

    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, we 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 derived 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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    File URL: http://arxiv.org/pdf/1011.4991
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1011.4991.

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    Date of creation: Nov 2010
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    Handle: RePEc:arx:papers:1011.4991

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    Web page: http://arxiv.org/

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