Tanja Magoc

The optimality of non-additive approaches for portfolio selection

The selection of assets in which to invest money is of critical importance in the finance industry, and is rendered very treacherous because of the inherent market fluctuations, and the connections with the Economy, and major world events. Because of the high dimensionality of the problem of selecting an optimal portfolio (in the financial sense of, a portfolio outperforming other portfolios), and the large amount of data available, intelligent systems (e.g. artificial intelligence techniques, machine learning approaches) are a natural approach to tackle this problem, from a computational standpoint. Numerous techniques have been developed to combine the values of return, risk, and other characteristics of an asset. However, the majority of techniques that have been used to construct a portfolio, tend to ignore dependencies among the characteristics of an asset. Moreover, most of the techniques assume that all available data are precise, which is not the case since, for instance, the expected return of an asset is a prediction of future behavior. To address these drawbacks, it was proposed in Magoc, Modave, Ceberio, and Kreinovich (2009) to use non-additive (or fuzzy) methods. Fuzzy methods outperformed other techniques, at least in the case of the Shanghai market, where full disclosure of information is assumed. In this paper, we give an intuition why fuzzy approach performs very well in this particular finance problem.

MPCT: media propelled computational thinking

Media-Propelled Computational Thinking (MPCT - pronounced impact) is a course designed to introduce programming in the context of engaging problems in media computation, math, and physics. Programming concepts are introduced as incremental steps needed to solve pragmatic problems students already understand. The problems, graphical API, and hands-on program features are intended to expose fundamental concepts in mathematics and quantitative science. MPCT is offered in an entering students program for freshmen who plan to specialize in a variety of STEM (science, technology, engineering and math) and non-STEM subjects. The curriculum is intended to strengthen student intuition and interest in mathematical modeling and programming by engaging students in the direct manipulation of simple mathematical systems that model and display familiar physical phenomena. MPCT uses programs as concrete and manipulatable examples of fundamental concepts to engage a diverse range of students including women and underrepresented minorities. Variants of MPCT are being developed for high schools, and as a means to introduce computational science to upper division undergraduates studying non-computational STEM disciplines. This paper provides an overview of MPCT and representative problem studies including models of ballistics and resonant systems. The evaluation plan is described and very preliminary results are presented.

Interval-based multi-criteria decision making: Strategies to order intervals

Ordering alternatives in interval-based multi- criteria decision making problems is not a trivial task when the intervals of preference are overlapping. In this paper, we aim at giving a rational and natural way of ranking alternatives by computing the degrees of preference, taking into consideration the upper and lower bounds of the interval of preference as well as its width. We slightly modify the general description of degree of preference to accommodate the strategy of choice for risk-prone and risk-averse individuals as well as situations where more information is available (e.g., a probability distribution over the intervals).

How to relate fuzzy and OWA estimates

In many practical situations, we have several estimates x<inf>1</inf>, …, x<inf>n</inf> of the same quantity x, i.e., estimates for which x<inf>1</inf> ≈ x, x<inf>2</inf> ≈ x, …, and x<inf>n</inf> ≈ x. It is desirable to combine (fuse) these estimates into a single estimate for x. From the fuzzy viewpoint, a natural way to combine these estimates is: (1) to describe, for each x and for each i, the degree μ≈(x<inf>i</inf>-x) to which x is close to x<inf>i</inf>, (2) to use a t-norm (“and”-operation) to combine these degrees into a degree to which x is consistent with all n estimates, and then (3) find the estimate x for which this degree is the largest. Alternatively, we can use computationally simpler OWA (Ordered Weighted Average) to combine the estimates x<inf>i</inf>. To get better fusion, we must appropriately select the membership function μ≈(x), the t-norm (in the fuzzy case) and the weights (in the OWA case). Since both approaches - when applied properly - lead to reasonable data fusion, it is desirable to be able to relate the corresponding selections. For example, once we have found the appropriate μ≈(x) and t-norm, we should be able to deduce the appropriate weights - and vice versa. In this paper, we describe such a relation. It is worth mentioning that while from the application viewpoint, both fuzzy and OWA estimates are not statistical, our mathematical justification of the relation between them uses results that have been previously applied to mathematical statistics.

A line of sight algorithm using fuzzy measures

A line of sight algorithm is an important tool in determining visibility of target points from an observer point. This method has found applications in real life problems such as urban planning, combat missions, and computer graphics simulations. Even though different line of sight algorithms have been developed for these purposes, they mostly rely only on the elevation of the terrain and are not extendable to consideration of other criteria. In this paper, we develop a new line of sight algorithm that allows numerous criteria to be considered when determining visibility of a point from another point. The novel line of sight algorithm uses fuzzy integration to take into consideration dependencies among numerous criteria considered.

Empirical formulas for economic fluctuations: Towards a new justification

To avoid crisis developments, it is important to make financial decisions based on the models which correct predict the probabilities of large-scale economic fluctuations. At present, however, most financial decisions are based on Gaussian random-walk models, models which are known to underestimate the probability of such fluctuations. There exist better empirical models for describing these probabilities, but economists are reluctant to use them since these empirical models lack convincing theoretical explanations. To enhance financial stability and avoid crisis situations, it is therefore important to provide theoretical justification for these (more) accurate empirical models. Such a justification is provided in this paper.

Selecting the Best Location for a Meteorological Tower: A Case Study of Multi-objective Constraint Optimization

Using the problem of selecting the best location for a meteorological tower as an example, we show that in multi-objective optimization under constraints, the traditional weighted average approach is often inadequate. We also show that natural invariance requirements lead to a more adequate approach – a generalization of Nash’s bargaining solution.

Computational Methods for Investment Portfolio: The Use of Fuzzy Measures and Constraint Programming for Risk Management

Computational intelligence techniques are very useful tools for solving problems that involve understanding, modeling, and analysis of large data sets. One of the numerous fields where computational intelligence has found an extremely important role is finance. More precisely, optimization issues of one’s financial investments, to guarantee a given return, at a minimal risk, have been solved using intelligent techniques such as genetic algorithm, rule-based expert system, neural network, and support-vector machine. Even though these methods provide good and usually fast approximation of the best investment strategy, they suffer some common drawbacks including the neglect of the dependence among among criteria characterizing investment assets (i.e. return, risk, etc.), and the assumption that all available data are precise and certain. To face these weaknesses, we propose a novel approach involving utility-based multi-criteria decision making setting and fuzzy integration over intervals.

Logit discrete choice model: a new distribution-free justification

According to decision making theory, if we know the user’s utility