Symmetric Duality in Mathematical Programming

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ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Mathematical Optimization Techniques

The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND

Higher moment models for risk and portfolio management

This thesis considers specific topics related to the dynamic modelling and management of risk, with a particular emphasis on the generation of asymmetric and fat tailed behavior observed in practise. Specifically, extensions to the dynamics of the popular GARCH model, to capture time variation in higher moments, are considered in the univariate and multivariate context, with a special focus on the Generalized Hyperbolic distribution. In Chapter 1, I consider the extension of univariate GARCH processes with higher moment dynamics based on the Autoregressive Conditional Density model of Hansen (1994), with conditional distribution the Generalized Hyperbolic. The value of such dynamics are analyzed in the context of risk management, and the question of ignoring them discussed. In Chapter 2, I review some popular multivariate GARCH models with a particular emphasis on the dynamic correlation model of Engle (2002), and alternative distributions such those from the Generalized Asymmetric Laplace of Kotz, Kozubowski, and Podgorski (2001). In Chapter 3, I propose a multivariate extension to the Autoregressive Conditional Density model via the independence framework of the Generalized Orthogonal GARCH models, providing the first feasible model for large dimensional multivariate modelling of time varying higher moments. A comprehensive out-of- sample risk and portfolio management application provides strong evidence of the improvement over non time varying higher moments. Finally, in Chapter 4, I consider the benefits of active investing when the benchmark index is not optimally weighted. I investigate advances in the definition and use of risk measures in portfolio allocation, and propose certain simple solutions to challenges arising in the optimization of these measures. Combining the models discussed in the previous chapters, within a fractional programming optimization framework and using a range of popular risk measures, a large scale out-of-sample portfolio application on the point in time constituents of the Dow Jones Industrial Average is presented and discussed, with clear implications for active investing and benchmark policy choice

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

Distributionally Robust Optimization: A Review

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization