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 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.
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.
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.
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 study the portfolio selection problem of a long-run investor who is maximising the asymptotic growth rate of her expected utility. We show that, somewhat surprisingly, it is essentially not affected by introduction of a floor constraint which requires the wealth process to dominate a given benchmark at all times. We…
The dominant energy condition imposes a restriction on initial value pairs found on a spacelike hypersurface of a Lorentzian manifold. In this article, we study the space of initial values that satisfy this condition strictly. To this aim, we introduce an index difference for initial value pairs and compare it to its c…
We consider a problem of optimal investment with intermediate consumption and random endowment in an incomplete semimartingale model of a financial market. We establish the key assertions of the utility maximization theory assuming that both primal and dual value functions are finite in the interiors of their domains a…
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.
We present a method for a certain class of Markov Decision Processes (MDPs) that can relate the optimal policy back to one or more reward sources in the environment. For a given initial state, without fully computing the value function, q-value function, or the optimal policy the algorithm can determine which rewards w…
Proves rigidity for specific initial data sets under the dominant energy condition.
problem Rigidity of initial data sets with boundary and convex polytopes.
method Solution of boundary value problems for Dirac operators and approximations by manifolds with smooth boundary.
result Proves rigidity for compact smooth spin manifolds and convex polytopes under the dominant energy condition.
Unified framework for efficient Frank-Wolfe optimization of Dominant Set Clustering.
problem Optimizing Dominant Set Clustering with various Frank-Wolfe algorithms.
method Unified framework for pairwise, standard, and away-steps Frank-Wolfe algorithms, with explicit convergence rates.
result Explicit convergence rates for Frank-Wolfe methods in Dominant Set Clustering.
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 consultative papers for the Basel II Accord require rating systems to provide a ranking of obligors in the sense that the rating categories indicate the creditworthiness in terms of default probabilities. As a consequence, the default probabilities ought to present a monotonous function of the ordered rating catego…
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 tackles robust knowledge transfer in parallel RL tasks.
problem Transfer knowledge from low-tier to high-tier tasks in parallel RL without shared dynamics or reward functions.
method Identifies Optimal Value Dominance condition and proposes online learning algorithms for both tasks.
result Achieves constant regret on partial states and near-optimal regret when tasks are dissimilar.
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…
Study analyzes climate-tech investments across 14 sectors.
problem Accelerating climate-tech innovation in nascent value chains.
method Analysis of 4,172 firms and 12,929 investments over 15 years.
result Only 15% of firms develop end products, 59% support them, and 26% develop services.
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 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.
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.
GPR ensemble method predicts stock returns efficiently.
problem Predicting stock returns using machine learning.
method Ensemble Gaussian Process Regression (GPR) for online learning.
result Method outperforms existing models in R-squared and Sharpe ratio. Paper introduces a new power-dominance axis in estimator design.
problem Estimator design trade-off between bias and variance.
method Introduces a third power regime, `power-dominant', with an unavoidable error penalty.
result Any estimator in the `power-dominant' regime is structurally sub-optimal.
We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function induces decreasing impatience, we establish the existence of an equilibrium through …
In this paper, we propose an information-theoretic exploration strategy for stochastic, discrete multi-armed bandits that achieves optimal regret. Our strategy is based on the value of information criterion. This criterion measures the trade-off between policy information and obtainable rewards. High amounts of policy …
We prove that a representation from the fundamental group of a closed surface of negative Euler characteristic with values in the isometry group of a Riemannian manifold of sectional curvature bounded by -1 can be dominated by a Fuchsian representation. Moreover, we prove that the domination can be made strict, unless …
This note removes technical assumptions and characterizes relatively dominated representations.
problem Geometrically finiteness and Anosov conditions in higher-rank settings.
method Characterization using eigenvalue gaps and limit maps.
result Relatively dominated representations are characterized using eigenvalue gaps and limit maps.
New method optimizes multiple objectives using particle dynamics and gradient flow.
problem Optimizing multiple conflicting objectives in complex scenarios.
method Interacting particle method combining Langevin and birth-death dynamics with a dominance potential.
result Method effectively relocates dominated particles, improving Pareto optimality.
Introduces Lambda Expected Shortfall as a risk measure generalizing ES.
problem Lack of a comprehensive risk measure that generalizes ES and Lambda-VaR.
method Introduces Lambda-ES, a new risk measure with explicit formula and properties.
result Lambda-ES is the smallest quasi-convex and law-invariant risk measure dominating Lambda-VaR.
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…
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.
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.
Study on convex ordering in stochastic control for swing contracts, proving value function convexity.
problem Pricing of swing contracts under stochastic dynamics.
method Discrete-time stochastic optimal control problem, convexity propagation, Brownian diffusion model, Stein's formula.
result Value function is convex in underlying asset price, relaxation of convexity assumption for semi-convexity.
Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents are drawn from admixtures of distributions over words, known as topics. The inference problem of recovering topics from admixtures, is NP-hard. Assuming separability, a strong assumption, [4] gave the first provable algorithm for inference. F…
In this work, we develop a novel framework to measure the similarity between dynamic financial networks, i.e., time-varying financial networks. Particularly, we explore whether the proposed similarity measure can be employed to understand the structural evolution of the financial networks with time. For a set of time-v…
TOPPO improves PPO for MTRL by balancing critic gradients, outperforming SAC.
problem Critic-side gradient ill-conditioning in PPO for MTRL.
method Critic Balancing modules to improve gradient conditioning and balance task updates.
result TOPPO achieves stronger mean and tail-task performance than SAC-family and ARS-family baselines.
Transaction costs appear in financial markets in more than one form. There are several results in the literature on small proportional transaction cost and not that many on fixed transaction cost. In the present work, we heuristically study the effect of both types of transaction cost by focusing on a portfolio optimiz…
This study presents a long-term alternative formula for stock price variation described by a geometric Brownian motion on the basis of median instead of mean or expected values. The proposed method is motivated by the observation made in remote fields, where optimality of bet-hedging or diversification strategies is ex…
This paper shows a buy-and-hold strategy is asymptotically log-optimal for a market with a dominant asset.
problem Finding a safe and optimal investment strategy in a market with a dominant asset.
method Investment strategy based on the dominant asset and buy-and-hold approach.
result Buy-and-hold strategy on the dominant asset is asymptotically log-optimal with a sublinear rate of convergence.
Risk diversification is one of the dominant concerns for portfolio managers. Various portfolio constructions have been proposed to minimize the risk of the portfolio under some constrains including expected returns. We propose a portfolio construction method that incorporates the complex valued principal component anal…
American options can be equivalent to European options under certain conditions.
problem Determining when American options can be simplified to European options.
method Using methods from Jourdain and Martini, Chrsitensen, and convex duality.
result A first step towards verifying representability of American options.
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.
This paper tackles noisy multi-objective optimization with adaptive resampling using bootstrapping.
problem Challenges in optimizing noisy multi-objective problems, especially trade-offs between exploration and exploitation.
method Adaptive resampling with bootstrapping to estimate probability of dominance and improve precision.
result Demonstrates the efficiency of the resampling approach in NSGA-II algorithm under multiple noise variations.
This paper extends Kelly Criterion to include rebalancing frequency for optimal portfolio selection.
problem Optimizing a portfolio with multiple assets and varying rebalancing frequency.
method Using Kelly Criterion, the paper derives necessary and sufficient conditions for the frequency-based Kelly optimal portfolio.
result Proves the necessity and sufficiency of conditions for the frequency-based Kelly optimal portfolio.
New insights into Bartnik mass from improvability of dominant energy scalar.
problem Characterizing Bartnik mass minimizing initial data sets.
method Introducing improvability concept, proving non-improvability consequences, and analyzing pp-wave counterexamples.
result Bartnik mass minimizing initial data sets are characterized, advancing conjectures.
Ridge regression performs optimally in noisy environments with heavy-tailed distributions.
problem Performance of ridge regression in noisy environments with heavy-tailed noise.
method Established excess risk bounds using integral operator framework and Fuk-Nagaev inequality.
result Ridge regression achieves optimal convergence rates under heavy-tailed noise, demonstrating robustness.
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 are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class (D) as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows…