Abstract.We consider optimization problems for minimizing conditional valueat-risk (CVaR) from a computational point of view, with an emphasis on financial applications. As a general solution approach, we suggest to reformulate these CVaR optimization problems as two-stage recourse problems of stochastic programming. Specializing the L-shaped method leads to a new algorithm for minimizing conditional value-at-risk. We implemented the algorithm as the solver CVaRMin. For illustrating the performance of this algorithm, we present some comparative computational results with two kinds of test problems. Firstly, we consider portfolio optimization problems with 5 random variables. Such problems involving conditional value at risk play an important role in financial risk management. Therefore, besides testing the performance of the proposed algorithm, we also present computational results of interest in finance. Secondly, with the explicit aim of testing algorithm performance, we also present comparative computational results with randomly generated test problems involving 50 random variables. In all our tests, the experimental solver, based on the new approach, outperformed by at least one order of magnitude all general-purpose solvers, with an accuracy of solution being in the same range as that with the LP solvers.
This chapter describes the capabilities and the usage of SLP-IOR, our interactive model management system for stochastic linear programming (SLP). The main features of SLP-IOR are the following: the system is intended to support the entire life cycle of a model, including model formulation, analysis of the model instance, solving it, and analyzing the solution. A main design characteristic is keeping connection to an algebraic modeling system; we have chosen GAMS [3,4]. This approach has the following advantages: on the one hand, the powerful general-purpose solvers connected to GAMS are available for solving deterministic equivalents of SLP problems; on the other hand, deterministic linear programs (LPs) formulated in the algebraic modeling language of GAMS can be imported into SLP-IOR to develop stochastic variants of these. However, the use of GAMS is optional; with the exception of the above-mentioned GAMS-related features, SLP-IOR can be fully utilized without having access to GAMS.From the functional point of view, SLP-IOR integrates three main groups of facilities. The core part serves for dealing with SLP model instances. The workbench component supports working with test problem batteries and performing test runs with them. The third component consists of a solver library organized as a solver description database and a collection of executables of solvers. Besides some general-purpose LP solvers, the solver library contains several solvers specialized to the various SLP model classes.The system runs under Windows 32. SLP-IOR itself has been developed in Borland Delphi 6 in an object-oriented style. The majority of our own solvers have been developed in Fortran using Compaq Visual Fortran 6.1.
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