A relaxed approach to combinatorial problems in robustness and diagnostics

in Statistics and Computing (2010), 20(1), 99-115

A range of procedures in both robustness and diagnostics require optimisation of a target functional over all subsamples of given size. Whereas such combinatorial problems are extremely difficult to solve ... [more ▼]

A range of procedures in both robustness and diagnostics require optimisation of a target functional over all subsamples of given size. Whereas such combinatorial problems are extremely difficult to solve exactly, something less than the global optimum can be ‘good enough’ for many practical purposes, as shown by example. Again, a relaxation strategy embeds these discrete, high-dimensional problems in continuous, low-dimensional ones. Overall, nonlinear optimisation methods can be exploited to provide a single, reasonably fast algorithm to handle a wide variety of problems of this kind, thereby providing a certain unity. Four running examples illustrate the approach. On the robustness side, algorithmic approximations to minimum covariance determinant (MCD) and least trimmed squares (LTS) estimation. And, on the diagnostic side, detection of multiple multivariate outliers and global diagnostic use of the likelihood displacement function. This last is developed here as a global complement to Cook’s (in J. R. Stat. Soc. 48:133–169, 1986) local analysis. Appropriate convergence of each branch of the algorithm is guaranteed for any target functional whose relaxed form is—in a natural generalisation of concavity, introduced here—‘gravitational’. Again, its descent strategy can downweight to zero contaminating cases in the starting position. A simulation study shows that, although not optimised for the LTS problem, our general algorithm holds its own with algorithms that are so optimised. An adapted algorithm relaxes the gravitational condition itself. [less ▲]

A robust heuristic for the optimal selection of a portfolio of stocks

in International Journal of Operational Research (2010), 9(3), 258-271

This paper introduces a new optimization heuristic for the robustification of critical inputs under consideration in many problems. It is shown that it allows to improve significantly the quality and the ... [more ▼]

This paper introduces a new optimization heuristic for the robustification of critical inputs under consideration in many problems. It is shown that it allows to improve significantly the quality and the stability of the results for two classical financial problems, i.e. the Markowitz' portfolio selection problem and the computation of the financial beta. Focus here is on the robust Minimum Covariance Determinant (MCD) estimator which can easily be substituted to the classical estimators of location and scatter. By definition, the computation of this estimator gives rise to a combinatorial optimization problem. We present a new heuristic, called 'RelaxMCD', which is based on a relaxation of the problem to the continuous space. The utility of this approach and the performance of our heuristic, with respect to other competitors, are illustrated through extensive simulations. [less ▲]

Informatique en Sciences de Gestion et en Sciences Economiques - Niveau 2

Learning material (2009)

Alternative to the Mean-Variance Asset Allocation Analysis: A Scenario Methodology for Portfolio Selection

in Gregoriou, Greg N. (Ed.) Stock Market Volatility (2009)

This paper introduces a new methodology to optimize the allocation of financial assets. The objective of the model is to maximize the expected return of the portfolio under constraints limiting its Value ... [more ▼]

This paper introduces a new methodology to optimize the allocation of financial assets. The objective of the model is to maximize the expected return of the portfolio under constraints limiting its Value-at-Risk. The assets could consist in stocks as well as options. We rely on a flexible scenario tree approach to represent the future prices. In order to reduce the number of leaves and maintain the model tractable, stocks prices are obtained through the Fama & French empirical asset pricing model. Experiments on historical data are performed to illustrate the method and show the performance of the approach. Different strategies are compared: considering various market distributions, several factor models and a few portfolio hypothesis. [less ▲]

Systèmes d'information de gestion modernes

Scientific conference (2008, December)

Informatique en Sciences de Gestion

Learning material (2005)

Solving the m-TSP Problem with Stochastic or Time Dependent Demands

in Opasanon, S.; Miller-Hooks, E. (Eds.) Proceedings of TRISTAN V (Triennial Symposium on Transportation Analysis) (2004, June)

There are many examples of problems in transportation where some elements are uncertain. In the distribution of goods as well as systems responding to calls for emergency, demands typically occur in a ... [more ▼]

There are many examples of problems in transportation where some elements are uncertain. In the distribution of goods as well as systems responding to calls for emergency, demands typically occur in a random fashion. Transportation systems have thus to be created in face of uncertainty about future levels of demands, making strategic decisions difficult to take. Similarly, traffic conditions vary randomly over time and travel routes are usually designed in face of uncertainty about traffic conditions, hence about effective travel times. Stochastic models, i.e. models that take uncertainty explicitly into account, have thus a central role to play in transportation. [less ▲]

Simulated annealing for complex portfolio selection problems

in European Journal of Operational Research (2003), 150(3), 546-571

This paper describes the application of a simulated annealing approach to the solution of a complex portfolio selection model. The model is a mixed integer quadratic programming problem which arises when ... [more ▼]

This paper describes the application of a simulated annealing approach to the solution of a complex portfolio selection model. The model is a mixed integer quadratic programming problem which arises when Markowitz' classical mean-variance model is enriched with additional realistic constraints. Exact optimization algorithms run into difficulties in this framework and this motivates the investigation of heuristic techniques. Computational experiments indicate that the approach is promising for this class of problems. (C) 2003 Elsevier B.V. All rights reserved. [less ▲]

Modelling Financial Data and Portfolio Optimization Problems

Doctoral thesis (2001)

This doctoral dissertation in management science, entitled “Modelling Financial Data and Portfolio Optimization Problems”, consists of two independent parts, whose unifying theme is the construction and ... [more ▼]

This doctoral dissertation in management science, entitled “Modelling Financial Data and Portfolio Optimization Problems”, consists of two independent parts, whose unifying theme is the construction and solution of mathematical programming models motivated by portfolio selection problems. As such, this work is located at the interface of operations research and of finance. It draws heavily on techniques and theoretical results originating in both disciplines. The first part of the dissertation (Chapter 2) deals with an extension of Markowitz model and takes into account some of the side-constraints faced by a decision-maker when composing an investment portfolio, viz. lower and upper bounds on the quantities traded, and upper bounds on the number of assets included in the portfolio. We focus on the algorithmic difficulties raised by this model and we describe an original simulated annealing heuristic for its solution. The second (and largest) part of the thesis deals with a new multiperiod model for the optimization of a portfolio of options linked to a single index (Chapters 4-10). The objective of the model is to maximize the expected return of the portfolio under constraints limiting its value-at-risk. The model contains several interesting features, like the possibility to rebalance the portfolio with options introduced at the start of each period, explicit consideration of transaction costs, realistic pricing of options, consideration of advanced probability models to represent the future, etc. Some deep theoretical results from the financial literature are exploited in order to enrich the model and to extend its applicability. In particular, several available schemes for the generation of scenarios and for option pricing have been critically examined, and the most appropriate ones have been implemented. Furthermore, several optimization approaches (heuristic or exact procedures) have also been developed, implemented and tested. The models investigated in the dissertation bear on very different portfolio problems, draw on separate streams of scientific literature, and are handled by distinct algorithmic techniques. Therefore, the corresponding parts of the dissertation are fully independent, and each part contains its own specific introduction and literature review. [less ▲]

Théorie stochastique de la décision d'investissement

Book published by De Boeck & Larcier (1997)

La complexité, l'imprévisibilité croissantes de l'environnement et de la structure interne des entreprises contraignent le gestionnaire à tendre vers une description probabiliste de l'univers. Le passage ... [more ▼]

La complexité, l'imprévisibilité croissantes de l'environnement et de la structure interne des entreprises contraignent le gestionnaire à tendre vers une description probabiliste de l'univers. Le passage de la théorie classique, paramétrique, incluant la variabilité des données dans un contexte déterministe et discret, à la théorie stochastique continue, se fait progressivement. Chaque étape est illustrée au moyen d'exemples concrets. Un logiciel (sur CD-ROM) permet la résolution immédiate des problèmes propres à l'utilisateur. [less ▲]