Algorithm for cardinality-constrained quadratic

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 illustration is provided.

Abstract. We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose mean–risk models which are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of second-order stochastic dominance. Next, we develop a specialized parametric method for recovering the entire mean–risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and realizations. 1.

This article investigates four models for minimizing the tracking error between the returns of a portfolio and a benchmark. Due to linear performance fees of fund managers, we can argue that linear deviations give a more accurate description of the investorsÕ risk attitude than squared deviations. All models have in common that absolute deviations are minimized instead of squared deviations as is the case for traditional optimization models. Linear programs are formulated to derive explicit solutions. The models are applied to a portfolio containing six national stock market indexes (USA,

The mathematical model of portfolio optimization is usually represented as a bicriteria optimization problem where a reasonable trade--o# between expected rate of return and risk is sought. In a classical Markowitz model the risk is measured by a variance, thus resulting in a quadratic programming model. As an alternative, the MAD model was proposed where risk is measured by (mean) absolute deviation instead of a variance. The MAD model is computationally attractive, since it is transformed into an easy to solve linear programming program. In this paper we present an extension to the MAD model allowing to account for downside risk aversion of an investor, and at the same time preserving simplicity and linearity of the original MAD model. Keywords: Portfolio Optimization, Downside Risk Aversion, Linear Programming -- iii -- About the Authors Wojtek Michalowski is a Senior Research Scholar with the Decision Analysis and Support Project at IIASA. Wlodzimierz Ogryczak is Associate Profes...

We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose mean--risk models which are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of second-order stochastic dominance. Next, we develop a specialized parametric method for recovering the entire mean--risk e#cient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and realizations.

review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. –ii– The mathematical model of portfolio optimization is usually represented as a bicriteria optimization problem where a reasonable trade–off between expected rate of return and risk is sought. In a classical Markowitz model the risk is measured by a variance, thus resulting in a quadratic programming model. As an alternative, the MAD model was proposed where risk is measured by (mean) absolute deviation instead of a variance. The MAD model is computationally attractive, since it is transformed into an easy to solve linear programming program. In this paper we present an extension to the MAD model allowing to account for downside risk aversion of an investor, and at the same time preserving simplicity and linearity of the

In this paper, we develop a framework for the modeling, analysis, and computation of solutions to multitiered financial network problems with intermediaries in which both the sources of financial funds as well as the intermediaries are multicriteria decision-makers. In particular, we assume that these decision-makers seek not only to maximize their net revenues but also to minimize risk with the risk being penalized by a variable weight. We make explicit the behavior of the various decision-makers, including the consumers at the demand markets for the financial products. We derive the optimality conditions, and demonstrate that the governing equilibrium conditions of the financial network economy can be formulated as a finite-dimensional variational inequality problem. Qualitative properties of the equilibrium financial flow and price pattern are provided. A computational procedure that exploits the network structure of the problem is proposed and then applied to several numerical examples.