New framework for ranking distributions using variable fractional parameters.
problem Ordering distributions with varying steepness and local non-concavities.
method Introducing a function γ:Ro[0,1] to replace the fixed parameter in fractional SD. result Enables ranking of a broader range of distributions and incorporates dynamic greediness.
We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …
The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
Proposes new rule for ranking investment prospects over long horizons.
problem Ranking investment prospects over long horizons considering bounded risk aversion.
method Introduces asymptotic fractional-order stochastic dominance with bounded relative risk aversion.
result Establishes equivalent conditions for the new rule under lognormal returns without mean non-negativity constraint.
New EI strategies using OWA and SSD for excess return.
problem Selecting EI portfolios that stochastically dominate a benchmark.
method Proposes a new OWA-based EI model and introduces a new SSD criterion.
result OWA-based EI portfolios stochastically dominate a benchmark and generate excess return.
Unexpectedly, weighted Pareto variables are stochastically dominant.
problem Understanding stochastic dominance in Pareto distributions.
method Analyzing weighted averages of Pareto random variables with infinite mean.
result The weighted average of Pareto variables is stochastically dominant.
New class of heavy-tailed distributions shows weighted averages dominate individual variables.
problem Understanding and comparing risks in heavy-tailed distributions.
method Introducing a new class of heavy-tailed distributions and proving stochastic dominance relations.
result Weighted averages of random variables in this class are stochastically larger than individual variables.
New method ranks multivariate distributions in SMOOP using q-dominance.
problem Lack of reliable methods to rank multivariate distributions in SMOOP.
method Introduces center-outward q-dominance and develops empirical test procedures.
result Proves q-dominance implies FSD and establishes a sample size threshold.
New characterization of second-order stochastic dominance with applications in risk management.
problem Characterizing second-order stochastic dominance.
method Properties of Expected Shortfall risk measures.
result New interpretation and proof techniques for second-order stochastic dominance.
Paper extends stochastic dominance for compound binomial distributions.
problem Stochastic dominance for infinite-mean random variables.
method Investigates properties and inclusion relationships of distribution classes, extends results to compound binomial distributions.
result Establishes necessary and sufficient conditions for first-order stochastic dominance preservation.
The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.
problem Comparing and characterizing random outcomes in risk assessment.
method Exploring the equivalence between higher order risk measures and stochastic dominance, using stochastic optimization and expectiles as examples.
result Higher order risk measures and stochastic dominance are equivalent and can be used to characterize random outcomes.
Solves risk minimization problem with SSD constraints.
problem Finding SSD-minimal quantile function under mixed constraints.
method Explicitly works out SSD-minimal solution and relates to Skorokhod problem.
result Explicit solution to risk minimizing problem.
Develops a new solver for optimizing with stochastic dominance constraints.
problem Optimizing with stochastic dominance constraints is computationally expensive and impractical.
method Introduces Light Stochastic Dominance Solver (light-SD) that uses Lagrangian properties and surrogate approximation.
result The light-SD solver demonstrates superior performance on various problems.
New method assesses multivariate stochastic dominance using Optimal Transport.
problem Benchmarking models across multiple metrics considering dependencies.
method Characterization of multivariate first stochastic dominance via couplings, entropic regularization, and Optimal Transport.
result Established CLT and consistency for the empirical statistic, enabling hypothesis testing.
New study shows diversification can increase risk for heavy-tailed losses.
problem Diversification can increase tail risk for heavy-tailed losses.
method Comparison of diversified portfolio to a 'one-basket' benchmark.
result Diversified portfolio has larger tail probabilities than a 'one-basket' benchmark for all thresholds.
Study max- and min-stability under first-order stochastic dominance, finding new functional characterizations.
problem Understanding max- and min-stability in stochastic dominance.
method Representation theorem for functionals satisfying max-stability, combining max- and min-stability to define Lambda-quantiles.
result New characterizations of functionals, including Lambda-quantiles, in finance and political science.
We derive properties of the cdf of random variables defined as saddle-type points of real valued continuous stochastic processes. This facilitates the derivation of the first-order asymptotic properties of tests for stochastic spanning given some stochastic dominance relation. We define the concept of Markowitz stochas…
Expands learning paradigm to stochastic orders using Choquet-Toland distance and Variational Dominance Criterion.
problem Learning high-dimensional distributions with stochastic orders.
method Introduces Choquet-Toland distance and Variational Dominance Criterion, uses input convex maxout networks (ICMNs).
result Proposes surrogates for Choquet-Toland distance and Variational Dominance Criterion with parametric rates.
Paper proposes a new method to compare classifiers across multiple datasets.
problem Comparing classifiers over multiple datasets with multiple criteria.
method Adopting decision theory, the paper introduces generalized stochastic dominance for ranking classifiers.
result Generalized stochastic dominance can be used to rank classifiers and statistically tested.
The paper explores arbitrage opportunities in derivative markets under specific conditions.
problem Arbitrage opportunities in derivative markets under different conditions.
method Analyzes the relationship between pricing kernel monotonicity and stochastic arbitrage opportunities.
result Pricing kernel nonmonotonicity is equivalent to stochastic arbitrage opportunities under adequacy.
Diversification improves profits for heavy-tailed investments.
problem Investment portfolios of Pareto-distributed returns.
method Stochastic dominance and majorization order.
result Diversification increases first-order stochastic dominance for heavy-tailed returns.
A new graphical method compares stochastic variables visually.
problem Comparing non-deterministic measurements visually.
method Cumulative distribution function dominance measure and quantile decomposition.
result Additional conclusions missed by other methods can be inferred.
We develop a new statistical test for comparing variables with varying scales.
problem Comparing variables with different scales in multidimensional spaces.
method Order based on expectations of random variables, generalized stochastic dominance (GSD) order, regularized statistical test, linear optimization, imprecise probability models.
result Validated through multidimensional data from various fields.
Paper establishes sufficient condition for comparing linear combinations of infinite-mean risks.
problem Comparing linear combinations of infinite-mean risks under stochastic dominance.
method Introduced a new class of distributions and used majorization order to compare weights.
result Linear combinations of random variables are stochastically larger when their weight vectors are smaller in majorization order.
This paper proposes a new clustering method based on Stochastic Dominance for asset allocation.
problem Traditional clustering methods fail to capture risk dominance relationships among assets.
method Integrates Stochastic Dominance theory with machine learning algorithms to construct a Stochastic Dominance Coefficient Matrix and modify clustering algorithms.
result The proposed method effectively facilitates customized asset allocation for investors.
Paper formalizes multi-dimensional FSD using geometric methods.
problem Complex measure theory and calculus barriers to formalization in proof assistants.
method Geometric framework for first-order stochastic dominance in N dimensions.
result Geometric approach bypasses complex integration theory for direct comparison of survival probabilities.
Local SGD outperforms minibatch SGD for quadratic objectives.
problem Theoretical foundations of local SGD are lacking.
method Proved local SGD strictly dominates minibatch SGD for quadratic objectives and accelerated local SGD is minimax optimal.
result Local SGD does not dominate minibatch SGD in general convex objectives.
New method amplifies hidden structure in complex networks.
problem Difficulty in uncovering hidden structure in complex networks.
method Iterative weakening of dominant structure through randomization.
result Theoretical support for the effectiveness of structure amplification.
This note finds closed-form solutions for mean-risk portfolios using a specific type of mixture distribution.
problem Finding optimal portfolios under mean-risk criteria for general distributions.
method Using normal mean-variance mixture (NMVM) distributions, the paper derives closed-form expressions for mean-risk frontiers by optimizing a Markowitz model with adjusted return vectors.
result Closed-form solutions for mean-risk portfolios are found for return vectors following NMVM distributions.
We solve S-shaped utility portfolio selection with SD constraints using algorithms and neural networks.
problem Optimizing portfolios with S-shaped utility functions under SD constraints.
method First-order SD constraint solution, numerical algorithm for SSD, neural network approach.
result Effective numerical and neural network solutions for SSD constrained problems.
Defines diversification as a binary relationship between financial portfolios.
problem Defines diversification in a new binary relationship for financial portfolios.
method Proposes a new definition of diversification based on convex linear combinations and second order stochastic dominance.
result The proposed definition coincides with second order stochastic dominance.
In this paper, we study and analyze the mini-batch version of StochAstic Recursive grAdient algoritHm (SARAH), a method employing the stochastic recursive gradient, for solving empirical loss minimization for the case of nonconvex losses. We provide a sublinear convergence rate (to stationary points) for general noncon…
The Mean-Variance Criterion is equivalent to Second-order Stochastic Dominance under symmetric Elliptical distributions.
problem Determining the equivalence of Mean-Variance Criterion and Stochastic Dominance Criteria.
method Analyzing under symmetric and Skew-Elliptical distributions using Monte Carlo simulations.
result The Mean-Variance Criterion does not coincide with Second-order Stochastic Dominance for some types of risk-averse investors.
New findings show ETO outperforms IEO in well-specified models with sufficient data.
problem Comparing estimate-then-optimize (ETO) and integrated-estimation-optimization (IEO) methods in stochastic optimization.
method Analyzes the performance of ETO and IEO in well-specified and misspecified models using stochastic dominance.
result Simple ETO outperforms IEO asymptotically in well-specified models with sufficient data.
We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide an asymptotic expansion up to explicit exponentially decaying terms. Our analysis…
Investigates Meyer risk measures and their applications in finance.
problem Existence and structure of Meyer risk measures.
method Fractional stochastic dominance and Meyer's utility function.
result Existence and structure of risk measures respecting v-SD order. Enhanced indexation with sector constraints using SSD for better portfolio performance.
problem Constructing a portfolio that outperforms a market index while respecting sector investment proportions.
method Subset second-order stochastic dominance (subset SSD) applied to asset subset constraints.
result Subset SSD approach outperforms S&P500 and standard SSD approaches.
New approach for prudent risk evaluation using model aggregation.
problem Risk evaluation and optimization under uncertainty.
method Model Aggregation (MA) approach based on stochastic dominance.
result Produces robust risk evaluation and distributional models.
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous …
A new optimization method reduces memory and compute requirements for deep learning.
problem Memory and compute constraints in second-order stochastic optimizers for deep learning.
method Proposes KrAD, a novel factorization to approximate inverse Fisher matrix without inversion, leading to KrADagrad.
result Improves performance over Shampoo for 32-bit precision and comparable/generalization on real datasets.
Stochastic Gradient Descent phases explained for deep networks.
problem Understanding the different regimes of SGD in deep learning.
method Teacher-student perceptron model, phase diagram analysis.
result SGD phases separated by batch size B∗, scaling with training set size P. Study finds monthly SIPs outperform first-day SIPs in Nifty 50 by 0.5-2.5% annually.
problem Underexplored impact of SIP timing in India's equity market.
method 22-year analysis using multi-layered statistical framework (non-parametric tests, effect size metrics, SSD).
result Monthly SIPs (EXP-SIP) outperform first-day SIPs (FTD-SIP) by 0.5-2.5% annually over short-to-medium-term horizons.
We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for asymptotic optimality of standard stochastic gradient procedures. Roughly, the n…
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed for deterministic objectives to the stochastic setting. Given an optimization me…
Deviation inequalities for stochastic approximation methods.
problem Establishing bounds on the deviation of stochastic approximation methods.
method Martingale approximation method for separately Lipschitz functions.
result Established various deviation inequalities for stochastic approximation by averaging and minimization.
Study on risk measures using distorted Choquet integrals with random distortions.
problem Developing risk measures under random distortions of capacities.
method Introducing and analyzing randomly distorted Choquet integrals with respect to a distorted capacity, establishing properties and providing representations.
result Representation of comonotonic additive conditional risk measures using G-randomly distorted Choquet integrals.
We develop a statistical framework to benchmark and select large language models based on their risks.
problem Benchmarking and selecting large language models based on their associated risks.
method A distributional framework using first and second order stochastic dominance, linked to mean-risk models in finance.
result Formalizes a risk-aware approach for model selection, balancing risk and utility.
In this paper, we study the stochastic combinatorial multi-armed bandit (CMAB) framework that allows a general nonlinear reward function, whose expected value may not depend only on the means of the input random variables but possibly on the entire distributions of these variables. Our framework enables a much larger c…