The construction of the best combination of investment instruments (investment portfolio) is a principal goal of investment policy. This is an optimization problem: select the best portfolio from all admissible portfolios. To approach this problem we have to choose the selection criterion first. The seminal paper of Markowitz [8] opened a new era in portfolio optimization. The paper formulated ...

The paper considers robust optimization to cope with uncertainty about the stock return process in one period option hedging problems. The robust approach relates portfolio choice to uncertainty, making more cautious hedges when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlying stocks and show that for this set the robust problem is a second ...

For various organizational reasons, large investors typically split their portfolio decision into two stages - asset allocation and stock selection. We hypothesise that mean-variance models are superior to equal weighting for allocation, while the reverse applies selection, as estimation errors less of a problem when used than confirm this hypothesis US data using Bayes-Stein with no short sale...

The mean-variance principle of Markowitz (1952) for portfolio selection gives disappointing results once the mean and variance are replaced by their sample counterparts. The problem is ampli…ed when the number of assets is large and the sample covariance is singular or nearly singular. In this paper, we investigate four regularization techniques to stabilize the inverse of the covariance matrix...

This work gives a brief overview of the portfolio selection problem following the mean-risk approach first proposed by Markowitz (1952). We consider various risk measures, i.e. variance, value-at-risk and expected-shortfall and we study the efficient frontiers obtained by solving the portfolio selection problem under these measures. We show that under the assumption that returns are normally di...

On the basis of Markowitz mean-variance framework, a new optimal portfolio selection approach is presented. The portfolio selection model proposed in the approach includes the expected return, the risk, and especially a quadratic type transaction cost of a portfolio. Using this model may yield an optimal portfolio solution that maximizes return, and minimizes risk, as well as also minimizes tra...

Mathematical programming methods dominate in the portfolio optimization problems, but they cannot be used if we introduce a constraint limiting the number of different assets included in the portfolio. To solve this model some of the heuristics methods (such as genetic algorithm, neural networks and particle swarm optimization algorithm) must be used. In this paper we utilize binary particle sw...