Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

Coherent ranging with Envisat radar altimeter: a new perspective in analyzing altimeter data using Doppler Processing

ESA's Envisat mission carried a RA-2 radar altimeter since its launch in 2002 to sense sea state and especially measure sea surface height (SSH). The onboard processing combined multiple echoes incoherently to reduce Speckle noise and benefit from data compression. In fact, according to past literature the amplitudes were generally expected to be independent. Nevertheless, samples of complex data time series of individual echoes (IE) were down-linked and archived since 2004 for research studies. In this note we demonstrate that there is sufficient inter-pulse coherence for Doppler processing and we suggest that the archived data can be re-processed into improved SSH. This is of particular interest in challenging domains (e.g., coastal zone) where coherent processing can mitigate errors from ocean surface backscatter inhomogeneity and nearby land backscatter. A new method called zero-Doppler to process IEs is thus proposed and discussed

A mixed integer linear program to compress transition probability matrices in Markov chain bootstrapping

Bootstrapping time series is one of the most acknowledged tools to study the statistical properties of an evolutive phenomenon. An important class of bootstrapping methods is based on the assumption that the sampled phenomenon evolves according to a Markov chain. This assumption does not apply when the process takes values in a continuous set, as it frequently happens with time series related to economic and financial phenomena. In this paper we apply the Markov chain theory for bootstrapping continuous-valued processes, starting from a suitable discretization of the support that provides the state space of a Markov chain of order k≥1. Even for small k, the number of rows of the transition probability matrix is generally too large and, in many practical cases, it may incorporate much more information than it is really required to replicate the phenomenon satisfactorily. The paper aims to study the problem of compressing the transition probability matrix while preserving the “law” characterising the process that generates the observed time series, in order to obtain bootstrapped series that maintain the typical features of the observed time series. For this purpose, we formulate a partitioning problem of the set of rows of such a matrix and propose a mixed integer linear program specifically tailored for this particular problem. We also provide an empirical analysis by applying our model to the time series of Spanish and German electricity prices, and we show that, in these medium size real-life instances, bootstrapped time series reproduce the typical features of the ones under observation. This is a post-peer-review, pre-copyedit version of an article published in Annals of Operations Research volume. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10479-016-2181-

Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

Some polynomial special cases for the Minimum Gap Graph Partitioning Problem

We study various polynomial special cases for the problem of partitioning a vertex-weighted undirected graph into p connected subgraphs with minimum gap between the largest and the smallest vertex weight

Uniform partition of graphs: Complexity results, algorithms and formulations

In this presentation, we address centered and non centered equipartition problems on graphs into p connected components (p-partitions). In the former case, each class of the partition must contain exactly one special vertex called center, whereas in the latter, partitions are not required to fulfil this condition. Among the different equipartition problems considered in the literature, we focus on: 1) Most Uniform Partition (MUP) and 2) Uniform Partition (UP). Both criteria are defined either w.r.t. weights assigned to each vertex or to costs assigned to each vertex-center pair. Costs are assumed to be flat, i.e., they are independent of the topology of the graph. With respect to costs, MUP minimizes the difference between the maximum and minimum cost of the components of a partition and UP refers to optimal min-max or max-min partitions. Additionally, we present various problems of partitioning a vertex-weighted undirected graph into p connected components minimizing the gap that is a measure related to the difference between the largest and the smallest vertex weight in the component of the partition. For all the problems considered here, we provide polynomial time algorithms, as well as, NP-complete results even on very special classes of graphs like trees. For the centered partitioning problems, we also present a new mathematical programming formulation that can be compared with the ones already provided in the literature for similar problems

Managing coastal aquifer salinity under sea level rise using rice cultivation recharge for sustainable land cover

Data Availability: No data was used for the research described in the article.Code availability: Upon request.Supplementary material is available online at https://www.sciencedirect.com/science/article/pii/S2214581823001532#sec0095 .Copyright © 2023 The Authors. Study region: The coastal aquifer of Nile Delta, Egypt is used to develop the current study. Study focus: Excess water from rice irrigation is a source of incidental recharge to mitigate seawater intrusion. This paper numerically explores the optimal location of rice cultivations by subdividing the delta domain into three distinct recharging regions (north, central and south). Additionally, SEAWAT code was simulated under a combination of rice cultivation relocation and sea level rise (SLR). New hydrological insights for the region: The study findings revealed significant variations in salt volume reduction depending on the location of rice cultivation in the delta. Placing rice cultivation in the northern region resulted in the highest reduction of salt volume (19 %). In contrast, locating the recharge in the central region yielded a salt volume reduction of 0.50 %, while rice cultivation in the southern region produced a 15 % increase. Considering the projected SLR of 61 cm by 2100, there was an overall salt volume increment of 3 %. However, when accounting for both SLR and rice cultivation recharge in the northern region, a substantial salt volume reduction of 17 % was observed. The results demonstrated that incidental recharge by rice cultivation in coastal aquifers is an effective method for enhancing saltwater intrusion control. Moreover, this study improves our understanding of hydrological processes and expected responses in the delta under future climate scenarios