Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM) model, where the assets are limited with the introduction of quantity and cardinality constraints.\ud
We propose a completely new approach for solving the LAM model based on a reformulation as a Standard Quadratic Program, on a new lower bound that we establish, and on other recent theoretical and computational results for such problem. These results lead to an exact algorithm for solving the LAM model for small size problems. For larger problems, such algorithm can be relaxed to an efficient and accurate heuristic procedure that is able to find the optimal or the best-known solutions for problems based on some standard financial data sets that are used by several other authors. We also test our method on five new data sets involving real-world capital market indices from major stock markets. We compare our results with those of CPLEX and with those obtained with very recent heuristic approaches in order to illustrate the effectiveness of our method in terms of solution quality and of computation time. All our data sets and results are publicly available for use by other researchers
A standard Quadratic Programming problem (StQP) consists in minimizing a (nonconvex) quadratic form over the standard simplex. For solving a SLQP we present an exact and a heuristic algorithm, that are based on new theoretical results for quadratic and convex optimization problems. With these results a StQP is reduced to a constrained nonlinear minimum weight clique problern in an associated graph. Such a Clique problem, which does not seem to have been Studied before, is then solved with all exact and a heuristic algorithm. Some computational experience shows that Our algorithms are able to solve StQP problems of at least one order of magnitude larger than those reported in the literature. (c) 2007 Elsevier B.V. All rights reserved
One recent and promising strategy for Enhanced Indexation is\ud
the selection of portfolios that stochastically dominate the benchmark.\ud
We propose here a new type of approximate stochastic dominance rule and\ud
we show that it implies other existing approximate stochastic dominance\ud
rules. We then use it to find the portfolio that approximately\ud
stochastically dominates a given benchmark with the best possible\ud
approximation. Our model is initially formulated as a Linear Program with\ud
exponentially many constraints, and then reformulated in a more compact\ud
manner so that it can be very efficiently solved in practice. This\ud
reformulation also reveals an interesting financial interpretation. We\ud
compare our approach with several exact and approximate stochastic\ud
dominance models for portfolio selection. An extensive empirical analysis\ud
on real and publicly available datasets shows very good out-of-sample\ud
performances of our model
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