Dynamic mean semi-variance portfolio selection
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
A Hamilton-Jacobi-Bellman approach to optimal trade execution
Applied Numerical Mathematics
Dynamic optimal portfolio with maximum absolute deviation model
Journal of Global Optimization
Fuzzy multi-period portfolio selection optimization models using multiple criteria
Automatica (Journal of IFAC)
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This paper is concerned with mean-variance portfolio selection problems in continuous-time under the constraint that short-selling of stocks is prohibited. The problem is formulated as a stochastic optimal linear-quadratic (LQ) control problem. However, this LQ problem is not a conventional one in that the control (portfolio) is constrained to take nonnegative values due to the no-shorting restriction, and thereby the usual Riccati equation approach (involving a "completion of squares") does not apply directly. In addition, the corresponding Hamilton--Jacobi--Bellman (HJB) equation inherently has no smooth solution. To tackle these difficulties, a continuous function is constructed via two Riccati equations, and then it is shown that this function is a viscosity solution to the HJB equation. Solving these Riccati equations enables one to explicitly obtain the efficient frontier and efficient investment strategies for the original mean-variance problem. An example illustrating these results is also presented.