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.
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.
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.
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 …
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.
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.
Exact second-order optimization for deep learning reduces computational cost and improves performance.
problem Inadequate use of second-order optimization methods in deep learning due to high computational cost and non-convexity.
method Developed an exact stochastic second-order Newton method that addresses the non-convexity issue and provides an expression for the stochastic Hessian.
result Exact second-order Newton direction formula and its application in deep learning datasets.
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.
New methods show sparse portfolios offer no advantage over mean-variance in diversification.
problem Investment diversification and risk management with sparse portfolios.
method Developed and implemented a new estimation procedure for sparse second-order stochastic spanning using a greedy algorithm and Linear Programming.
result No benefit from expanding a sparse opportunity set beyond 45 assets; optimal sparse portfolio reduces tail risk.
Study finds risk sharing without convexity assumptions.
problem Finding fair risk allocations among agents with heterogeneous beliefs.
method Combines local comonotone improvement with Dieudonné-type argument.
result Existence of Pareto optima without convexity assumption.
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.
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.
We refine Expected Shortfall by controlling different tail portions, offering tailored risk assessments.
problem Risk assessment in financial positions, especially in tail regions.
method Introducing adjusted Expected Shortfall measures that control different tail portions.
result Adjusted Expected Shortfall measures ensure risk does not exceed specified thresholds for various probability levels.
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.
We consider the problem of sequential learning from categorical observations bounded in [0,1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise. We establish that, conditioned upon identical data with at least two observatio…
We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic dominance (SSD) relation. This compares the inherent dispersion of random retur…
The paper optimizes portfolios by selecting financial ratios via PCA for better value investment.
problem Embedding value investment in portfolio optimization models.
method Principal Component Analysis (PCA) to filter out dominant financial ratios, then applying portfolio optimization model with second-order stochastic dominance criteria.
result PCA-SPO(B) strategy outperforms other models in terms of downside deviation, CVaR, VaR, Sortino, Rachev, and STARR ratios.
Enhanced indexation uses equity and index options for better performance.
problem Improving portfolio performance through enhanced indexation.
method Integrating index options into an enhanced indexation strategy based on second-order stochastic dominance.
result Introducing option strategies in enhanced indexation leads to improved out-of-sample performance.
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.
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. 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.
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second order statistics of the data, are far less prevalent despite strong theoretical pro…
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.
Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff. Economic intuition suggests that high risk aversion leads to a rather concentrated distribution, whereas lower ris…
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.
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.
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.
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is non-dominated. We propose studying this p…
In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal stationary points. However, existing results on stochastic non-convex optimizatio…
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.
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.
Paper uses second-order differential geometry to study stochastic mechanics.
problem Stochastic differential equations and their symmetries.
method Develops second-order differential geometry to study symmetries of SDEs and constructs stochastic mechanics.
result Establishes stochastic Lagrangian and Hamiltonian mechanics and their relations with HJB equations.
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.
Investment strategy optimizes risk using a specific risk measure.
problem Optimizing investment with risk controlled by a weighted entropic risk measure.
method Investigation of expected utility maximization and risk minimization problems with solutions provided iteratively.
result Explicit characterization of solutions to optimization 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.
Paper proposes a second-order method for faster SVI convergence.
problem Poor convergence rate of first-order SVI algorithms.
method Derives Hessian matrix and implements two numerical schemes for efficient second-order SVI.
result Proposed approach achieves faster convergence compared to first-order SVI.
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…
New method explains predictive uncertainty by focusing on second-order effects.
problem Explaining predictive uncertainty in machine learning models.
method CovLRP, CovGI, etc., based on second-order effects.
result Predictive uncertainty is dominated by second-order effects.
New algorithm finds approximate stationary points in non-convex optimization.
problem Finding approximate stationary points in non-convex stochastic optimization.
method Design of an algorithm using O(ε−3) stochastic gradient and Hessian-vector products. result Optimal rate of O(ε−3) for finding ε-approximate stationary points, matching lower bounds. Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations which describe the motion of financial prices with respect to real world probabi…
AdaSub optimizes with second-order info in low-dims subspace.
problem Efficiently use second-order optimization methods with low computational cost.
method Adaptive subspace selection for second-order optimization.
result AdaSub outperforms other stochastic optimizers in time and iterations.
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we …
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are nonlinear generalisations of the…
In stochastic gradient descent, especially for neural network training, there are currently dominating first order methods: not modeling local distance to minimum. This information required for optimal step size is provided by second order methods, however, they have many difficulties, starting with full Hessian having…
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.