A memetic approach that combines a genetic algorithm (GA) and quadratic programming is used to address the problem of optimal portfolio selection with cardinality constraints and piecewise linear transaction costs. The framework used is an extension of the standard Markowitz mean–variance model that incorporates realistic constraints, such as upper and lower bounds for investment in individual ...

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 ...

Recently, several optimization approaches for portfolio selection have been proposed in order to alleviate the estimation error in the optimal portfolio. Among such are the normconstrained variance minimization and the robust portfolio models. In this paper, we examine the role of the norm constraint in the portfolio optimization from several directions. First, it is shown that the norm constra...

In 2014 the main tendency of Ukrainian economy was the losing of great deposit value. In this article we wish to explore a deposit portfolio structure in macroeconomic instability. We applied two approaches to the standard optimization portfolio: risk minimization for a given maximum return and return maximization for a given maximum risk. Of the two approaches to the standard optimization prob...

In this paper we develop tight bounds on the expected values of several risk measures that are of interest to us. This work is motivated by the robust optimization models arising from portfolio selection problems. The basic setting is to find a portfolio which maximizes (respectively minimizes) the expected utility (respectively disutility) values, in the midst of infinitely many possible ambig...

Portfolio optimization is one of the most important issues for effective and economic investment. There is plenty of research in the literature addressing this issue. Most of these pieces of research attempt to make the Markowitz’s primary portfolio selection model more realistic or seek to solve the model for obtaining fairly optimum portfolios. An efficient frontier in the ...

We consider the problem of portfolio selection, with transaction costs and constraints on exposure to risk. Linear transaction costs, bounds on the variance of the return, and bounds on different shortfall probabilities are efficiently handled by convex optimization methods. Problems with transaction costs that include a fixed fee, or discount breakpoints, cannot be directly solved by convex op...

The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which transaction costs are incurred to rebalance an investment portfolio. The Markowitz framework of mean-variance efficiency is used with costs modelled as a percentage of the value transacted. Each security in the por...

To solve a partial differential equation (PDE) numerically, we formulate it as a polynomial optimization problem (POP) by discretizing it via a finite difference approximation. The resulting POP satisfies a structured sparsity, which we can exploit to apply the sparse SDP relaxation of Waki, Kim, Kojima and Muramatsu [20] to the POP to obtain a roughly approximate solution of the PDE. To comput...