Robust estimation, regression and ranking with applications in portfolio optimization

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 108-112).Classical methods of maximum likelihood and least squares rely a great deal on the correctness of the model assumptions. Since these assumptions are only approximations of reality, many robust statistical methods have been developed to produce estimators that are robust against the deviation from the model assumptions. Unfortunately, these techniques have very high computational complexity that prevents their application to large scale problems. We present computationally efficient methods for robust mean-covariance estimation and robust linear regression using special mathematical programming models and semi-definite programming (SDP). In the robust covariance estimation problem, we design an optimization model with a loss function on the weighted Mahalanobis distances and show that the problem is equivalent to a system of equations and can be solved using the Newton-Raphson method. The problem can also be transformed into an SDP problem from which we can flexibly incorporate prior beliefs into the estimators without much increase in the computational complexity. The robust regression problem is often formulated as the least trimmed squares (LTS) regression problem where we want to nd the best subset of observations with the smallest sum of squared residuals. We show the LTS problem is equivalent to a concave minimization problem, which is very hard to solve. We resolve this difficulty by introducing the maximum trimmed squares" problem that finds the worst subset of observations. This problem can be transformed into an SDP problem that can be solved efficiently while still guaranteeing that we can identify outliers.(cont.) In addition, we model the robust ranking problem as a mixed integer minimax problem where the ranking is in a discrete uncertainty set. We use mixed integer programming methods, specifically column generation and network flows, to solve the robust ranking problem. To illustrate the power of these robust methods, we apply them to the mean-variance portfolio optimization problem in order to incorporate estimation errors into the model.by Tri-Dung Nguyen.Ph.D

Data-driven satisficing measure and ranking

We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of risk measures, we consider problems constrained by general convex risk measures and specifically by Conditional value-at-risk. Starting from offline optimization, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimization case, we develop primal-dual stochastic approximation algorithms respectively for general risk constrained problems, and derive their regret bounds. For both offline and online cases, we illustrate the relationship between risk ranking accuracy with sample size (or iterations).Comment: 26 Pages, 6 Figure

Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması

Mean-variance portfolio optimization model, introduced by Markowitz, provides a fundamental answer to the problem of portfolio management. This model seeks an efficient frontier with the best trade-offs between two conflicting objectives of maximizing return and minimizing risk. The problem of determining an efficient frontier is known to be NP-hard. Due to the complexity of the problem, genetic algorithms have been widely employed by a growing number of researchers to solve this problem. In this study, a literature review of genetic algorithms implementations on mean-variance portfolio optimization is examined from the recent published literature. Main specifications of the problems studied and the specifications of suggested genetic algorithms have been summarized

Optimal Portfolio Management in Alaska: A Case Study on Risk Characteristics of Environmental Consulting Companies

A Project Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE in Project ManagementSharp declines in global oil prices have led to a marked contraction in Alaska’s natural resource dependent economy. This, coupled with record the State’s budgetary shortfalls and a decrease in incoming federal dollars, has created a climate where environmental consulting companies must accept riskier projects to balance portfolio growth and security. As a result, companies must adopt a risk-based portfolio management approach as both a high level strategy and a core management practice. It is important to specifically identify projects best suited for an organization’s tolerance for risk based off of the supply and demand of the industry in rapidly changing economic conditions. Therefore, the aims of this project report are to help environmental consulting companies identify risk characteristics and manage their portfolio, as well as develop a tool to guide decision-making and selecting projects best suited for a companies’ portfolio strategy. The results of this research may provide Alaska based environmental companies with a clear understanding of the types of projects that offer both development and financial security for an organization. This research paper will present the methodology, results, and an environmental consulting portfolio management tool.Title Page / Table of Contents / List of Exhibits / Abstract / Introduction / Background / Literature Review / Project Methodology / Research Methodology / Presentation and Analysis of Data from Survey / Data Validation From Survey / Conclusion / Recommendation / Project Conclusion / Recommendations for Further Research / References / Appendi

Multi crteria decision making and its applications : a literature review

This paper presents current techniques used in Multi Criteria Decision Making (MCDM) and their applications. Two basic approaches for MCDM, namely Artificial Intelligence MCDM (AIMCDM) and Classical MCDM (CMCDM) are discussed and investigated. Recent articles from international journals related to MCDM are collected and analyzed to find which approach is more common than the other in MCDM. Also, which area these techniques are applied to. Those articles are appearing in journals for the year 2008 only. This paper provides evidence that currently, both AIMCDM and CMCDM are equally common in MCDM

A variable neighborhood search simheuristic for project portfolio selection under uncertainty

With limited nancial resources, decision-makers in rms and governments face the task of selecting the best portfolio of projects to invest in. As the pool of project proposals increases and more realistic constraints are considered, the problem becomes NP-hard. Thus, metaheuristics have been employed for solving large instances of the project portfolio selection problem (PPSP). However, most of the existing works do not account for uncertainty. This paper contributes to close this gap by analyzing a stochastic version of the PPSP: the goal is to maximize the expected net present value of the inversion, while considering random cash ows and discount rates in future periods, as well as a rich set of constraints including the maximum risk allowed. To solve this stochastic PPSP, a simulation-optimization algorithm is introduced. Our approach integrates a variable neighborhood search metaheuristic with Monte Carlo simulation. A series of computational experiments contribute to validate our approach and illustrate how the solutions vary as the level of uncertainty increases