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A priori optimization
 Operations Research
, 1990
"... Algorithm for cardinalityconstrained quadratic ..."
Optimization with stochastic dominance constraints
 SIAM Journal on Optimization
"... 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 the ..."
Abstract

Cited by 32 (5 self)
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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.
Frontiers of stochastically nondominated portfolios
 Econometrica
, 2003
"... 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 secondorder ..."
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Cited by 15 (3 self)
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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 secondorder 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.
A linear model for tracking error minimization
 Journal of Banking and Finance
, 1998
"... 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. A ..."
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Cited by 6 (0 self)
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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,
Extending the MAD Portfolio Optimization Model to Incorporate Downside Risk Aversion
, 1998
"... 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 ..."
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Cited by 3 (0 self)
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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
Financial Networks with Intermediation: Risk Management with Variable Weights
, 2004
"... 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 decisionmakers. In particular, we assume that the ..."
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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 decisionmakers. In particular, we assume that these decisionmakers 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 decisionmakers, 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 finitedimensional 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.
ThC16.4 Portfolio Optimization as a Learning Platform for Control Education and Research
"... Abstract — This paper demonstrates the use of discrete time portfolio optimization as a mechanism for introducing students to key problems in systems theory: control, system identification, model reduction, and verification. Too often students are not introduced to systems theory until very late in ..."
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Abstract — This paper demonstrates the use of discrete time portfolio optimization as a mechanism for introducing students to key problems in systems theory: control, system identification, model reduction, and verification. Too often students are not introduced to systems theory until very late in their programs, frequently after they have already decided on majors and generated momentum toward specific career plans. One reason for this late introduction is the prerequisite material demanded by our systems courses, typically involving a chain of math, physics, and engineering courses. Using portfolio optimization as the vehicle for introducing systems theory, however, can provide an early introduction to some of the central issues in the field. In particular, the openloop nature of portfolio optimization simplifies the decisionmaking context sufficiently to make these problems accessible to younger students. Moreover, the familiarity of financial decision making, regardless of technical background, allows a broad range of students to appreciate the importance and nature of these problems. Here we illustrate these ideas, using portfolio optimization to show how the presence of uncertainty and complexity in decision problems interconnect control, system identification, model reduction, and verification in the design of practical decision systems. I.