We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustra...

Multistage portfolio optimization models are difficult to solve when market risk is measured by Value-at-Risk (VaR), this paper proposes a soft method for solving VaR-based portfolio optimization models based on a soft optimization approach. In order to demonstrate the validity of the proposed soft method, we perform portfolio management experiments with real data from the New York stock market...

 Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral am...

This paper develops an approximate closed-form optimal portfolio allocation formula for a spot asset whose variance follows GARCH(1,1) process. We consider investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected from terminal wealth under Heston and Nandi (2000) GARCH (HN-GARCH) model. Based on approximation of log returns Campbell Viceira (1999), we obta...

The purpose of this study is to develop portfolio optimization and assets allocation using our proposed models. The study is based on a non-parametric efficiency analysis tool, namely Data Envelopment Analysis (DEA). Conventional DEA models assume non-negative data for inputs and outputs. However, many of these data take the negative value, therefore we propose the MeanSharp-βRisk (MShβR) model...

Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying t...