Portfolio selection under distributional uncertainty: A relative robust CVaR approach

Robust optimization, one of the most popular topics in the field of optimization and control since the late 1990s, deals with an optimization problem involving uncertain parameters. In this paper, we consider the relative robust conditional value-at-risk portfolio selection problem where the underlying probability distribution of portfolio return is only known to belong to a certain set. Our approach not only takes into account the worst-case scenarios of the uncertain distribution, but also pays attention to the best possible decision with respect to each realization of the distribution. We also illustrate how to construct a robust portfolio with multiple experts (priors) by solving a sequence of linear programs or a second-order cone program.     

A dual-interval vertex analysis method and its application to environmental decision making under uncertainty

In this study, a dual-interval vertex analysis (DIVA) method is developed, through incorporating the vertex method within an interval-parameter programming framework. The developed DIVA method can tackle uncertainties presented as dual intervals that exist in the objective function and the left- and right-hand sides of the modeling constraints. An interactive algorithm and a vertex analysis approach are proposed for solving the DIVA model. Solutions under an associated α-cut level can be generated by solving a series of deterministic submodels. They can help quantify relationships between the objective function value and the membership grade, which is meaningful for supporting in-depth analyses of tradeoffs between environmental and economic objectives as well as those between system optimality and reliability. A management problem in terms of regional air pollution control is studied to illustrate applicability of the proposed approach. The results indicate that useful solutions for planning the air quality management practices have been generated. They can help decision makers to identify desired pollution-abatement strategies with minimized costs and maximized environmental efficiencies.     

Pairs selection and outranking: An application to the S&P 100 index

Pairs trading is a popular quantitative speculation strategy. This article proposes a general and flexible framework for pairs selection. The method uses multiple return forecasts based on bivariate information sets and multi-criteria decision techniques. Our approach can be seen as a sort of forecast combination but the output of the method is a ranking. It helps to detect potentially under- and overvalued stocks. A first application with S&P 100 index stocks provides promising results in terms of excess return and directional forecasting.     

US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology

We study the problem of suitably locating US Coast Guard air stations to respond to emergency distress calls. Our goal is to identify robust locations in the presence of uncertainty in distress call locations. Our analysis differs from the literature primarily in the way we model this uncertainty. In our optimization and simulation based methodology, we develop a statistical model and demonstrate our procedure using a real data set of distress calls. In addition to guiding strategic decisions of placement of various stations, our methodology is also able to provide guidance on how the resources should be allocated across stations.     

A non-interactive elicitation method for non-linear multiattribute utility functions: Theory and application to agricultural economics

Practical implementation of Multiattribute Utility Theory is limited, partly for the lack of operative methods to elicit the parameters of the Multiattribute Utility Function, particularly when this function is not linear. As a consequence, most studies are restricted to linear specifications, which are easier to estimate and to interpret. We propose an indirect method to elicit the parameters of a non-linear utility function to be compatible with the observed behaviour of decision makers, rather than with their answers to direct surveys. The idea rests on approaching the parameter estimation problem as a dual of the decision problem by making the observed decisions to be compatible with a rational decision making process.     

Range-based Multi-Actor Multi-Criteria Analysis: A combined method of Multi-Actor Multi-Criteria Analysis and Monte Carlo simulation to support participatory decision making under uncertainty

Concerns about environmental and social effects have made Multi-Criteria Decision Making (MCDM) increasingly popular. Decision making in complex contexts often – possibly always – requires addressing an aggregation of multiple issues to meet social, economic, legal, technical, and environmental objectives. These values at stake may affect different stakeholders through distributional effects characterized by a high and heterogeneous uncertainty that no social actors can completely control or understand. On this basis, we present a new process framework that aims to support participatory decision making under uncertainty: the range-based Multi-Actor Multi-Criteria Analysis (range-based MAMCA). On the one hand, the process framework explicitly considers stakeholders’ objectives at an output level of aggregation. On the other hand, by means of a Monte Carlo analysis, the method also provides an exploratory scenario approach that enables the capture of the uncertainty, which stems from the complex context evolution. Range-based MAMCA offers a unique participatory process framework that enables us (1) to identify the alternatives pros and cons for each stakeholder group; (2) to provide probabilities about the risk of supporting mistaken, or at least ill-suited, decisions because of the uncertainty regarding to the decision-making context; (3) to take the decision-makers’ limited control of the actual policy effects over the implementation of one or several options into account. The range-based MAMCA framework is illustrated by means of our first case study that aimed to assess French stakeholders’ support for different biofuel options by 2030.     

A finite algorithm for monotone regression and the application of its principle to the aggregation of ranks and indifference curve fitting

Monotone regression makes optimal consistent adjusted value assignments to ordinal dependent data, or monotonically adjusts ratio-level-dependent variable data to achieve the best possible agreement with an explanatory linear (in the sense of parameters) model. Thus, for example, as a tool for building group or individual multi-attribute value (MAV) functions, it partially obviates the need to prespecify a particular MAV function class. The height of the unknown MAV function at each comparison bundle is determined along with the other model parameters.In this paper, the Kruskal stress criterion and iterative computational methodology are shown to be reducible to one of three simpler convex quadratic programming problems. The fundamental idea underlying the method is not restricted to least-squares objectives. An application to the problem of aggregation of ranks is shown. Here, the minimax data-fitting criterion is employed.     

On the worst scenario method: A modified convergence theorem and its application to an uncertain differential equation

We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient. This research was supported in part by the project MSM4781305904 from the Ministry of Education, Youth and Sports of the Czech Republic.     

On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: A general approach

The Homotopy Analysis Method of Liao [Liao SJ. Beyond perturbation: introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall/CRC Press; 2003] has proven useful in obtaining analytical solutions to various nonlinear differential equations. In this method, one has great freedom to select auxiliary functions, operators, and parameters in order to ensure the convergence of the approximate solutions and to increase both the rate and region of convergence. We discuss in this paper the selection of the initial approximation, auxiliary linear operator, auxiliary function, and convergence control parameter in the application of the Homotopy Analysis Method, in a fairly general setting. Further, we discuss various convergence requirements on solutions.