Extending the MAD Portfolio Optimization Model to Incorporate Downside Risk Aversion

The mathematical model of portfolio optimization is usually expected as a bicriteria optimization problem where a reasonable trade-off between expected rate of return 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

Modular Optimizer for Mixed Integer Programming MOMIP Version 1.1

This Working Paper documents the Modular Optimizer for Mixed Integer Programming (MOMIP). MOMIP is an optimization solver for middle-size mixed integer programming problems, based on a modified branch-and-bound algorithm. It is designed as part of a wider linear programming modular library being developed within the IIASA CSA project on "Methodology and Techniques of Decision Analysis". The library is a collection of independent modules, implemented as C++ classes, providing all the necessary functions of data input, data transfer, problem solution, and results output. The Input/Output module provides data structure to store a problem and its solution in a standardized form as well as standard input and output functions. All the solver modules take the problem data from the Input/Output module and return the solutions to this module. Thus, for straightforward use, one can configure a simple optimization system using only the Input/Output module and an appropriate solver module. More complex analysis may require use of more than one solver module. Moreover, for complex analysis of real-life problems, it may be more convenient to incorporate the library modules into an application program. This will allow the user to proceed with direct feeding of the problem data generated in the program and direct withdrawal results for further analysis. The paper provides the complete description of the MOMIP module. Methodological background allows the user to understand the implemented algorithm and efficient use of its control parameters for various analyses. The module description provides all the information necessary to make MOMIP operational. It is additionally illustrated with a tutorial example and a sample program. Modeling recommendations are also provided, explaining how to built mixed integer models in order to speedup the solution process. These may be interesting, not only for the MOMIP users, but also for users of any mixed integer programming software

Processing second-order stochastic dominance models using cutting-plane representations

This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)

DINAS - Dynamic Interactive Network Analysis System, v.3.0

This paper describes the methodological background and user manual of the Dynamic Interactive Network Analysis System (DINAS) which enables the solution of various multiobjective transshipment problems with facility location using IBM-PC XT/AT microcomputers. DINAS utilizes an extension of the classical reference point approach to handling multiple objectives. In this approach the decision-maker forms his requirements in terms of aspiration and reservation levels, i.e., he specifies acceptable and required values for given objectives. A special TRANSLOC solver was developed to provide DINAS with solutions to single-objective problems. It is based on the branch and bound scheme with a pioneering implementation of the simplex special ordered network (SON) algorithm with implicit representation of the simple and variable upper bounds (VUB & SUB). DINAS is prepared as a menu-driven and easy in usage system armed with a special network editor which reduces to minimum effort associated with input a real-life problem. Version 3.0 is highly compatible with the previous one. Differences between these versions are small, resulting from the introduction of some new features into the system

Dynamic Interactive Network Analysis System - DINAS Version 2.1 (1988). User's Manual

This paper is one of the series of 11 Working Papers presenting the software for interactive decision support and software tools for developing decision support systems. These products constitute the outcome of the contracted study agreement between the System and Decision Sciences Program at IIASA and several Polish scientific institutions. The theoretical part of these results is presented in the IIASA Working Paper WP-88-071 entitled "Theory, Software and Testing Examples in Decision Support Systems". This volume contains the theoretical and methodological backgrounds of the software systems developed within the project. This paper describes the methodological background and user manual of the Dynamic Interactive Network Analysis System (DINAS) which enables the solution of various multiobjective transshipment problems with facility location. DINAS utilizes an extension of the classical reference point approach to handling multiple objectives. A special TRANSLOC solver was developed to provide DINAS with solutions to single-objective problems. It is based on the branch and bound scheme with a new implementation of the simplex special ordered network (SON) algorithm with implicit representation of the simple and variable upper bounds (VUB & SUB). DINAS has been designed as a menu-driven and user-friendly system armed with a special network editor which reduces to minimum effort associated with defining real-life problems

Overview of Methods Implemented in MCA: Multiple Criteria Analysis of Discrete Alternatives with a Simple Preference Specification

Many methods have been developed for multiple criteria analysis and/or ranking of discrete alternatives. Most of them require complex specification of preferences. Therefore, they are not applicable for problems with numerous alternatives and/or criteria, where preference specification by the decisin makers can hardly be done in a way acceptable for small problems, e.g., for pair-wise comparisons. In this paper we describe several new methods implemented for a real-life application dealing with multi-criteria analysis of future energy technologies. This analysis involves large numbers of both alternatives and criteria. Moreover, the analysis was made by a large number of stakeholders without expeience in analytical methods. Therefore a simple method for interactive preference specification was condition for the analysis. The paper provides overview of several of new methods based on diverse concepts developed for multicriteria analysis, and summarizes a comparison of methods and experence of using them

Multiple Criteria Analysis of Discrete Alternatives with a Simple Preference Specification: Pairwise-outperformance based Approaches

Many methods have been developed for multiple criteria analysis and/or ranking of discrete alternatives. Most of them require complex specification of preferences. Therefore, they are not applicable for problems with numerous alternatives and/or criteria, where preference specification by the decision makers can hardly be done in a way acceptable for small problems, e.g., for pair-wise comparisons. In this paper we describe several new methods implemented for a real-life application dealing with muti-criteria analysis of future energy technologies. This analysis involves large numbers of both altrnatives and criteria. Moreover, the analysis was made by a large number of stakeholders without expeience in analytical methods. Therefore, a simple method for interactive preference specification was a condition for the analysis. The paper presents a number of new methods based on the developed out performance aggregations that take into account inter-alternative factors. Finally, a comparison of methods and experience of using them is discussed

A recursive procedure for selecting optimal portfolio according to the MAD model

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 a recursive procedure which allows to identify optimal portfolio of the MAD model depending on investor's downside risk aversion