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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
Provable randomized rounding for minimum-similarity diversification
When searching for information in a data collection, we are often interested not only in finding relevant items, but also in assembling a diverse set, so as to explore different concepts that are present in the data. This problem has been researched extensively. However, finding a set of items with minimal pairwise similarities can be computationally challenging, and most existing works striving for quality guarantees assume that item relatedness is measured by a distance function. Given the widespread use of similarity functions in many domains, we believe this to be an important gap in the literature. In this paper we study the problem of finding a diverse set of items, when item relatedness is measured by a similarity function. We formulate the diversification task using a flexible, broadly applicable minimization objective, consisting of the sum of pairwise similarities of the selected items and a relevance penalty term. To find good solutions we adopt a randomized rounding strategy, which is challenging to analyze because of the cardinality constraint present in our formulation. Even though this obstacle can be overcome using dependent rounding, we show that it is possible to obtain provably good solutions using an independent approach, which is faster, simpler to implement and completely parallelizable. Our analysis relies on a novel bound for the ratio of Poisson-Binomial densities, which is of independent interest and has potential implications for other combinatorial-optimization problems. We leverage this result to design an efficient randomized algorithm that provides a lower-order additive approximation guarantee. We validate our method using several benchmark datasets, and show that it consistently outperforms the greedy approaches that are commonly used in the literature.Peer reviewe
Learning to Generate Posters of Scientific Papers
Researchers often summarize their work in the form of posters. Posters
provide a coherent and efficient way to convey core ideas from scientific
papers. Generating a good scientific poster, however, is a complex and time
consuming cognitive task, since such posters need to be readable, informative,
and visually aesthetic. In this paper, for the first time, we study the
challenging problem of learning to generate posters from scientific papers. To
this end, a data-driven framework, that utilizes graphical models, is proposed.
Specifically, given content to display, the key elements of a good poster,
including panel layout and attributes of each panel, are learned and inferred
from data. Then, given inferred layout and attributes, composition of graphical
elements within each panel is synthesized. To learn and validate our model, we
collect and make public a Poster-Paper dataset, which consists of scientific
papers and corresponding posters with exhaustively labelled panels and
attributes. Qualitative and quantitative results indicate the effectiveness of
our approach.Comment: in Proceedings of the 30th AAAI Conference on Artificial Intelligence
(AAAI'16), Phoenix, AZ, 201
Tight steady-state availability bounds using the failure distance concept
Continuous-time Markov chains are commonly used for dependability modeling of repairable
fault-tolerant computer systems. Realistic models of non-trivial fault-tolerant systems often have very large state spaces. An attractive approach for dealing with the largeness problem is the use of pruningmethods with error bounds. Several such methods for computing steady-state
availability bounds have been proposed recently. This paper presents a new method which exploits the failure distance concept to bound more efficiently the behavior in the non-generated state space. It is proved that the bounding method gives tighter bounds than previous methods.
Numerical analysis shows that the new bounds can be significantly tighter.Postprint (published version
A biobjective method for sample allocation in stratified sampling
The two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs. In stratified random sampling, the sample size must be allocated to strata in order to optimize both objectives. In this note we address, following a biobjective methodology, this allocation problem. A two-phase method is proposed to describe the set of Pareto-optimal solutions of this nonlinear integer biobjective problem. In the first phase, all supported Pareto-optimal solutions are described via a closed formula, which enables quick computation. Moreover, for the common case in which sampling costs are independent of the strata, all Pareto-optimal solutions are shown to be supported. For more general cost structures, the non-supported Pareto-optimal solutions are found by solving a parametric knapsack problem. Bounds on the criteria can also be imposed, directing the search towards implementable sampling plans. Our method provides a deeper insight into the problem than simply solving a scalarized version,
whereas the computational burden is reasonable.Ministerio de Ciencia y TecnologĂ
Financial Applications of Semidefinite Programming: A Review and Call for Interdisciplinary Research
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