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OPTIMAL LOT SOLUTION TO CARDINALITY CONSTRAINED MEAN–VARIANCE FORMULATION FOR PORTFOLIO SELECTION
Author(s) -
Li Duan,
Sun Xiaoling,
Wang Jun
Publication year - 2006
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2006.00262.x
Subject(s) - portfolio , mathematical optimization , merton's portfolio problem , portfolio optimization , selection (genetic algorithm) , cardinality (data modeling) , modern portfolio theory , efficient frontier , computer science , post modern portfolio theory , mathematics , replicating portfolio , economics , econometrics , finance , data mining , artificial intelligence
The pioneering work of the mean–variance formulation proposed by Markowitz in the 1950s has provided a scientific foundation for modern portfolio selection. Although the trade practice often confines portfolio selection with certain discrete features, the existing theory and solution methodologies of portfolio selection have been primarily developed for the continuous solution of the portfolio policy that could be far away from the real integer optimum. We consider in this paper an exact solution algorithm in obtaining an optimal lot solution to cardinality constrained mean–variance formulation for portfolio selection under concave transaction costs. Specifically, a convergent Lagrangian and contour‐domain cut method is proposed for solving this class of discrete‐feature constrained portfolio selection problems by exploiting some prominent features of the mean–variance formulation and the portfolio model under consideration. Computational results are reported using data from the Hong Kong stock market.