A maximal domain for weak stochastic dominance strategy-proofness of the extended probabilistic serial correspondence

When the underlying probability distribution in a stochastic optimization is observed only through data, various data-driven formulations have been studied to obtain approximate optimal solutions. We show that no such formulations can, in a sense, theoretically improve the statistical quality of the solution obtained from empirical optimization. We argue this by proving that the first order behavior of the optimality gap against the oracle best solution, which includes both the bias and variance, for any data-driven solution second order stochastically dominates that from empirical optimization as long as suitable smoothness holds with respect to the underlying distribution. We demonstrate this impossibility of improvement in examples ranging across regularized optimization, distributionally robust optimization, parametric optimization, and Bayesian generalizations. We also discuss the connections of our results to other perspectives in statistics and data-driven optimization and illustrate practical implications in choosing among data-driven formulations. This paper was accepted by J. George Shanthikumar, data science. Funding: This work was supported by the National Science Foundation Division of Information and Intelligent Systems [Grant 1849280] and Division of Civil, Mechanical, and Manufacturing Innovation [Grant 1834710]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.04482 .

Factor of iid’s through stochastic domination

Environmental drivers and ecological processes underlying microbial community zonation in deep-sea polymetallic nodule sediments.

Portfolio Optimization with Robust Stochastic Dominance Testing: A Genetic Algorithm Approach

This study assesses the quality of local public administration in European cities using an analytical algorithm based on the B-TOPSIS approach. It draws on the Quality of Life in European Cities survey, which includes five questions on citizens’ satisfaction with local administration, rated on a simplified four-point verbal scale with an option to skip. To process this type of group data, the study extends B-TOPSIS to handle ordinal scales, uncertainty, and missing responses. The method is applied to data from 2023 and compared with 2019 to detect temporal changes in satisfaction. The framework compensates for incomplete information, integrates a Monte Carlo-based protocol for robust results, enhances the ranking through almost first-order stochastic dominance, and supports cross-survey comparison. The results show that Zurich, Luxembourg, and Antalya rank highest in satisfaction, while Rome and Palermo rank lowest. Residents of medium-sized and very large cities report higher satisfaction, with EU and EFTA cities outperforming those in the Western Balkans. Overall, satisfaction levels have remained stable since 2019. These findings offer both methodological contributions and practical insights into governance quality and sustainability, constructing a unified performance index from dispersed survey responses.

This paper optimizes a mixed-asset portfolio (MAP) of stocks, bonds, and direct real estate investments (DREIs) using the third-degree stochastic dominance (TSD) criterion. Hence, by introducing DREIs, we analyze improvements in the efficient frontiers of “super-convex” TSD (SCTSD)–dominant stocks-only portfolios and MAPs of stocks and bonds. Portfolio optimization based on the TSD criterion considers investors’ risk aversion and skewness preferences, which is particularly useful for applications with non-normal return distributions, one of the characteristics of real estate markets. The conditional value-at-risk (CVaR) at several confidence levels is used as an objective function when calculating the efficient frontiers in a quadratic optimization problem. We find that introducing DREIs and bonds separately and together leads to significant improvements in efficient frontiers of SCTSD-dominant MAPs compared to SCTSD-dominant portfolios of stocks only. The relative decrease in CVaR at a 95% confidence level amounted to ∼20% to 30% for the three-asset SCTSD-dominant lowest-risk MAP compared to the stocks-only SCTSD-dominant lowest-risk portfolio depending on a selected subset of DREIs. Optimization tests by including indirect real estate investments (REITs) show that low-risk efficient portfolios are still largely dominated by DREIs but REIT inclusion improves noticeably risk–return characteristics of the high-return end of the MAP efficient frontier.

On expectiles and almost stochastic dominance

BackgroundSeasonal behavioral divergence in zokors, driven primarily by their reproductive cycle, results in distinct ecological strategies between breeding and non-breeding periods. To elucidate how intestinal microbes adapt to these behavioral shifts, we used metagenomics to characterize the seasonal variations in the intestinal microbes of Eospalax rothschildi, a subterranean zokor endemic to China.ResultsMetagenomics revealed that summer samples showed an increased proportion of carbohydrate-degrading bacteria. Moreover, a significant difference in taxonomic composition was observed between the samples collected in the two seasons. Functional analysis based on the KEGG and CAZy databases revealed stronger carbohydrate degradation capacities in summer samples, notably through enhanced galactose metabolism capabilities. The enhanced galactose metabolism capabilities observed in summer were predominantly driven by increased abundance of α-galactosidase and β-galactosidase genes from enriched microbial populations, particularly Bacteroides, unclassified_f_Lachnospiraceae, Roseburia, and Faecalibacterium. Furthermore, iCAMP analysis revealed that deterministic and stochastic processes jointly governed intestinal microbial assembly in E. rothschildi during summer, as elevated nutritional demands potentially intensified host selection in the breeding season. Conversely, stochastic dominance in autumn may align with relaxed host selection.ConclusionsCollectively, these results demonstrated that season played a crucial role in modulating the composition, function, and assembly process of the intestinal microbes of E. rothschildi.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12866-025-04414-5.

Stochastic dominance has not been employed too often in practice due to its important limitations. To increase its versatility, the concept has recently been adapted by introducing various indices that measure the degree to which one probability distribution stochastically dominates another. In this article, starting from the fundamentals and using very simple examples, we present and discuss some of these indices when one intends to maintain invariance through increasing functions. This naturally leads to consideration of the appealing common representation, θ ( F , G ) = P ( X > Y ) , where ( X , Y ) is a random vector with marginal distributions F and G. The indices considered here arise from different dependencies between X and Y. This includes the case of independent marginals, as well as other indices related to a contamination model or to a joint quantile representation. We emphasize the complementary role of some of these indices, which, in addition to measuring disagreement with respect to stochastic dominance, enable us to describe the maximum possible difference in the status of a value x ∈ R under F or G. We apply these indices to simulated and real-world datasets, exploring their practical advantages and limitations. The tour includes lesser-known facets of well-known statistics such as Mann-Whitney, one-tailed Kolmogorov-Smirnov and Galton’s rank statistics, even providing additional theory for the latter.

Dynamic portfolio optimization under stochastic dominance: impact of investment frequency and bankroll management

Abstract We reconsider the foundations of expected utility without assuming the linearity of the independence axiom. We consider a decision-maker who cancels out common outcomes when comparing a pair of lotteries with the same probability tree. We show that if the decision-maker is consistent with first-order stochastic dominance or topological continuity in weak convergence, then the decision-maker is an expected utility maximizer. First, this offers a simple method to differentiate behavior between prospect theory, canceling out common outcomes, and cumulative prospect theory, satisfying first-order stochastic dominance. Second, this offers a novel method to test technical continuity assumptions based on their behavioral content.

Abstract According to Stochastic Dominance, it is rationally obligatory to prefer one gamble to another if it gives you the same chances of getting final outcomes you prefer. According to Statewise Maximality, it is rationally permissible not to disprefer a gamble if it is guaranteed not to result in a final outcome you disprefer. These principles conflict in cases involving incomplete preferences, known as Opaque Sweetening cases. In this paper, we argue for Stochastic Dominance and against Statewise Maximality in Opaque Sweetening cases. First, we rebut two standard arguments for statewise maximality, which we call the Argument from Full Information and the Argument from the Primacy of Final Outcomes. We then provide an argument for the verdict of Stochastic Dominance in Opaque Sweetening cases. This argument appeals to the principle of Transitivity, the Sure-Thing Principle, and the claim that stochastic reasoning is appropriate at least for choices which do not involve incomparability.

Abstract This paper introduces the general ideas for parametric integral stochastic orders, with which a continuum of parametric functions are defined as a bridge between different classes of non-parametric functions. This approach allows one to identify a parametric function class over which two given random variables may violate the non-parametric stochastic order with specific patterns. The parameter used to name the parametric function class also measures the ratio of dominance violation for the corresponding non-parametric stochastic orders. Our framework, expanding the domain of stochastic orders, covers the existing studies of almost stochastic dominance. This leads to intuitive explanations and simpler proofs of existing results and their extensions.

Abstract In this paper we review several optimization problems under uncertainty that can be represented as the problem of finding the optimal rearrangement of a matrix. By rearrangement we mean a permutation of the order of the elements in each column of the matrix, such that each column turns out to be oppositely ordered to the sum of the others. A simple heuristic iterative procedure called the Rearrangement Algorithm has been designed to find rearranged matrices so that the vector of their rowsums is minimal in the so-called Schur order, a notion connected to convex stochastic dominance, and to provide approximations to the solutions of various challenging problems with uncertainty scenarios. By changing the initial design of the matrix, or by introducing a family of matrices to be rearranged simultaneously, or by rearranging the columns in a prescribed way or in blocks, the Rearrangement Algorithm can be adapted to deal with several applications in a variety of fields including: the assembly line crew scheduling problem with uncertain labour times, the multi-way partitioning problem, the computation of dependence uncertainty bounds in finance, the fair allocation of indivisible items, and the estimation of a joint distribution subject to statistical uncertainty.

Hydraulic regimes-driven microbial community assembly and network stability in drinking water distribution systems: Mechanistic linkages with transport distance and stagnation effects.

Cyanobacterial blooms restructure suspended particulate matters and associated microbial community networks to regulate estrogen biodegradation in eutrophic freshwater lakes.

Green Investments in Portfolio Allocation: Combining Mean-Variance, Genetic Algorithms, and Stochastic Dominance

ABSTRACT Knowing if the stock market is efficient is important for investors, policymakers, researchers, and society as a whole, as it impacts investment strategies, capital allocation, market integrity, policy decisions, risk management, and economic efficiency. While Mean-Variance analysis has been a cornerstone of modern portfolio theory, stochastic dominance offers a complementary approach that better captures investor preferences taking behavioral considerations into account. This paper aims to provide a new outlook on the efficiency of the Brazilian stock market, using a different approach from the commonly used Mean-Variance analysis. We present evidence of the Brazilian stock market efficiency tests using data from the Bovespa Index (iBovespa) spot and futures, with maturity dates in 2, 4, and 6 months, using two different approaches: Mean-Variance (MV) and Stochastic Dominance (SD). The results show that the Brazilian stock market presents inefficiencies and the iBovespa spot is dominant over its futures. A robustness check corroborates our main findings that investors choosing the spot over the future will gain more utility when making this investment choice.

In this paper, we perform Markowitz stochastic dominance (MSD) efficiency tests on several international market indices and their corresponding ETFs against their constituent shares. We focus on major global market indices, such as the S&P500, FTSE 100, DAX 40, and Nikkei 225. We find in a rolling-window analysis that our tests reject MSD efficiency in more than 90% of the cases for indices and ETFs. Therefore, we construct optimal MSD portfolios of constituent stocks and assess their performance against the market indices and ETFs. The out-of-sample empirical results suggest that the optimal portfolios of investors with Markowitz-type preferences outperform both indices and ETFs while generating more than double the values of Sharpe ratios.