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

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

2010-11-23

arxiv.org/abs/1011.4991v1

Economy

Quantitative Finance

Portfolio Management

20 pages, 4 figures

Scientific paper

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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