A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems

Precision-Recall Curves Using Information Divergence Frontiers

Despite the tremendous progress in the estimation of generative models, the development of tools for diagnosing their failures and assessing their performance has advanced at a much slower pace. Recent developments have investigated metrics that quantify which parts of the true distribution is modeled well, and, on the contrary, what the model fails to capture, akin to precision and recall in information retrieval. In this paper, we present a general evaluation framework for generative models that measures the trade-off between precision and recall using R\'enyi divergences. Our framework provides a novel perspective on existing techniques and extends them to more general domains. As a key advantage, this formulation encompasses both continuous and discrete models and allows for the design of efficient algorithms that do not have to quantize the data. We further analyze the biases of the approximations used in practice.Comment: Updated to the AISTATS 2020 versio

Discrete bisector function and Euclidean skeleton in 2D and 3D

International audienceWe propose a new definition and an exact algorithm for the discrete bisector function, which is an important tool for analyzing and filtering Euclidean skeletons. We also introduce a new thinning algorithm which produces homotopic discrete Euclidean skeletons. These algorithms, which are valid both in 2D and 3D, are integrated in a skeletonization method which is based on exact transformations, allows the filtering of skeletons, and is computationally efficient

The Relationship between Saccadic Choice and Reaction Times with Manipulations of Target Value

Choosing the option with the highest expected value (EV; reward probability × reward magnitude) maximizes the intake of reward under conditions of uncertainty. However, human economic choices indicate that our value calculation has a subjective component whereby probability and reward magnitude are not linearly weighted. Using a similar economic framework, our goal was to characterize how subjective value influences the generation of simple motor actions. Specifically, we hypothesized that attributes of saccadic eye movements could provide insight into how rhesus monkeys, a well-studied animal model in cognitive neuroscience, subjectively value potential visual targets. In the first experiment, monkeys were free to choose by directing a saccade toward one of two simultaneously displayed targets, each of which had an uncertain outcome. In this task, choices were more likely to be allocated toward the higher valued target. In the second experiment, only one of the two possible targets appeared on each trial. In this task, saccadic reaction times (SRTs) decreased toward the higher valued target. Reward magnitude had a much stronger influence on both choices and SRTs than probability, whose effect was observed only when reward magnitude was similar for both targets. Across EV blocks, a strong relationship was observed between choice preferences and SRTs. However, choices tended to maximize at skewed values whereas SRTs varied more continuously. Lastly, SRTs were unchanged when all reward magnitudes were 1×, 1.5×, and 2× their normal amount, indicating that saccade preparation was influenced by the relative value of the targets rather than the absolute value of any single-target. We conclude that value is not only an important factor for deliberative decision making in primates, but also for the selection and preparation of simple motor actions, such as saccadic eye movements. More precisely, our results indicate that, under conditions of uncertainty, saccade choices and reaction times are influenced by the relative expected subjective value of potential movements

Students' Achievement Emotions and Online Learning in Teacher Education

Online learning has become widely accepted and is considered as an important approach that can overcome the limitations of on-campus learning, especially in higher education. The acceptance of learning technologies generally depends on technology related beliefs and the perceived ease of use. It can be assumed that students' emotional experiences, among other factors, have an impact on their use of learning technology. Although research on emotions in technology-supported learning environments has increased in recent years, the question how students experience online learning environments emotionally, and how these emotions are intervened with technology acceptance has not yet been answered in more detail. Up to now, only a limited number of studies has focused on emotions and technology acceptance of university students, especially in teacher education. Therefore, the purpose of this study is to analyze students' technology acceptance and achievement emotions after participating in an online course (in comparison to an on-campus course) in teacher education. Survey data from 182 students (88 of them participated in an on-campus course, 94 students attended an online course) revealed a higher level of positive emotions than of negative emotions, regardless of the learning environment. Students who attended the online course reported a higher level of boredom, anxiety, and anger, but less enjoyment. Furthermore, the results show that online students reported significantly higher levels of achievement task value and technological control. Technological value correlated significantly with enjoyment. In contrast to the theoretical assumptions, no systematic differences were found between the two learning environments for the achievement emotions hope, shame, hopelessness, and anxiety. Regardless of the learning environment, enjoyment was essential for the value that students attach to both, learning content and technology. The online and the on-campus group differed in terms of domain specific achievement outcome. However, these differences cannot be explained by the covariates, the two control and value scales, the technology related beliefs, and age. Main results of the study regarding the control-value theory and implications for online learning environments, as well as limitations of the study are presented and discussed

Combinatorial models for topology-based geometric modeling

Many combinatorial (topological) models have been proposed in geometric modeling, computational geometry, image processing or analysis, for representing subdivided geometric objects, i.e. partitionned into cells of different dimensions: vertices, edges, faces, volumes, etc. We can distinguish among models according to the type of cells (regular or not regular ones), the type of assembly ("manifold" or "non manifold"), the type of representation (incidence graphs or ordered models), etc