Study robust utility maximization with uncertain endowments.
problem Optimal strategy under nondominated model uncertainty.
method General representation result, Choquet's capacitability theorem, medial limits.
result Existence of optimal strategy and dual representation for optimal utility.
New method for superhedging without assuming continuous claims.
problem Superhedging without assuming upper semicontinuous contingent claims.
method Established a generalized duality for model-free superhedging using Choquet's capacitability theorem.
result Generalized duality for superhedging given marginal distributions without continuity assumptions.
New findings on null measurability in symmetrization interface of VC learning.
problem Null measurability issues in symmetrization interface of VC learning.
method Formalized in Lean 4, using Choquet capacitability and patching properties.
result Null-measurable bad event not Borel measurable, separating regularity levels.
In the paper we give necessary and sufficient conditions for the Jensen inequality to hold for the generalized Choquet integral with respect to a pair of capacities. Next, we apply obtained result to the theory of risk aversion by providing the assumptions on utility function and capacities under which an agent is risk…
Choquet regularization improves exploration in RL.
problem Improving exploration in reinforcement learning.
method Introducing Choquet regularizers to measure and manage exploration, reformulating RL problems and deriving explicit solutions.
result Explicit optimal distributions and Choquet regularizers for various exploratory samplers.
New risk measures for quantiles under ambiguity improve risk sharing.
problem Risk optimization under ambiguity using quantiles.
method Introducing Choquet quantiles and Choquet Expected Shortfall.
result Optimal allocations for quantile agents under ambiguity.
Choquet and minimax expectations are equivalent in European option pricing.
problem Pricing European options in incomplete markets.
method Comparing Choquet and minimax expectations in the context of European options.
result Choquet and minimax expectations are equal for European options.
The paper introduces risk consistency properties for credit ratings.
problem Promoting prudent investment decisions in credit ratings.
method Introducing and studying risk consistency properties in the framework of Choquet rating criteria.
result Characterization of Choquet risk measures and rating criteria satisfying risk consistency properties.
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.
Paper proposes a new classifier for gender detection in mobile telematics.
problem Detecting gender through mobile telematics data.
method Choquet fuzzy integral vertical bagging classifier combining random forest and rough set theory.
result Choquet fuzzy integral vertical bagging classifier outperforms other classifiers.
Short-time existence for the Einstein-Euler and the vacuum Einstein equations is proven using a Friedrich inspired formulation due to Choquet-Bruhat and York, where the system is cast into a symmetric hyperbolic form and the Riemann tensor is treated as one of the fundamental unknowns of the problem. The reduced system…
In this paper, we define a new capacity which allows us to control the behaviour of the Dirichlet spectrum of a compact Riemannian manifold with boundary, with "small" subsets (which may intersect the boundary) removed. This result generalizes a classical result of Rauch and Taylor ("the crushed ice theorem"). In the s…
Motivated by recent work of Choquet-Bruhat, Chrusciel, and Martin-Garcia, we prove monotonicity properties and comparison results for the area of slices of the null cone of a point in a Lorentzian manifold. We also prove volume comparison results for subsets of the null cone analogous to the Bishop-Gromov relative volu…
Neural LNS improves vehicle routing performance.
problem Optimizing vehicle routes with constraints.
method Integrates deep learning with large neighborhood search.
result Significantly outperforms existing methods on CVRP.
Proves properties of maximal hypersurfaces in specific spacetimes.
problem Maximal hypersurfaces in asymptotically AdS spacetimes.
method Uniqueness, existence, and regularity results via mathematical proofs.
result Proves uniqueness, existence, and regularity of maximal hypersurfaces.
Modeling reinsurance market, we find subgame perfect Nash equilibria.
problem Optimizing reinsurance market with multiple insurers and reinsurers.
method Sequential game with Subgame Perfect Nash Equilibria analysis.
result Characterized subgame perfect Nash equilibria in some market cases.
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 revises power theory using classical mechanics concepts.
problem Clarifying instantaneous power definitions for circuit elements.
method Defines power using classical mechanics concepts like velocity and momentum.
result General and compact expression for inductance, capacitance, and resistance powers.
Study transverse measures on infinite type hyperbolic surfaces.
problem Characterize the cone of transverse measures on infinite type hyperbolic surfaces.
method Use inverse limits and geodesic laminations to describe and construct cones of transverse measures.
result Explicit descriptions and bases of cones of transverse measures exist for many laminations.
This paper reviews incompatibilities of comonotonic risk measures.
problem Incompatibilities of comonotonic risk measures with central properties.
method Literature review and Choquet representation of comonotonic additive risk measures.
result Comonotonic additive risk measures cannot be surplus invariant.
Dual representation of Kantorovich functional using martingale measures.
problem Representation of Kantorovich functional on Skorokhod space.
method Choquet capacity generated by martingale measures with constraints.
result Dual representation of Kantorovich functional.
Paper introduces a new risk measure that considers risk aversion.
problem Risk management and variability assessment.
method Extended Gini Shortfall risk measure using Choquet integral representations.
result The new risk measure is coherent and captures variability.
Deep learning improves cECG denoising for better cardiac health monitoring.
problem Motion artifacts limit the clinical use of cECG for long-term monitoring.
method End-to-end deep learning architecture trained on motion-corrupted cECG and reference ECG.
result MSE of 0.167 and Cross Correlation of 0.476 for signal denoising.
Paper tackles inventory management with deep learning, improving performance and adherence to constraints.
problem Managing inventory with limited resources and constraints.
method Proposes a novel method to sample from a distribution of possible constraint paths, extends exo-IDP formulation, introduces neural coordinator, and uses modified DirectBackprop algorithm.
result Deep reinforcement learning policies with a neural coordinator outperform classic baselines in terms of performance and adherence to constraints.
In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is shown that the only arbitrage-free price functional that fulfills some additional mild requirements is the integral of the unit zero-coupon b…
Recursive KalmanNet generalizes well in noisy, out-of-distribution scenarios.
problem Generalization in noisy, out-of-distribution scenarios.
method Recurrent neural network guided by a Kalman filter.
result Recursive KalmanNet performs well in scenarios with different temporal dynamics from training data.
A framework for reinforcement learning tackles CVRP with competitive results.
problem Optimizing routes for vehicles with limited capacity.
method Formulates action selection as a mixed-integer optimization problem, uses policy iteration to improve policies.
result Achieves an average gap of 1.7% with state-of-the-art OR methods on CVRP instances.
The paper proves local isometric embeddings for singular metrics near a point.
problem Existence of local isometric embeddings for singular Riemannian metrics.
method Ramified local isometric embeddings using Leray's ramified Cauchy-Kovalevskaya Theorem.
result Existence of local analytic isometric embeddings into Euclidean space.
Model-free preference under ambiguity defined and applied.
problem Understanding and quantifying ambiguity aversion and prudence.
method Introduces a new model-free definition of ambiguity attitudes and applies it in various contexts.
result New definition of ambiguity prudence equivalent to specific mathematical functions.
Sym-NCO leverages symmetricities to improve DRL-NCO performance.
problem Improving neural combinatorial optimization methods.
method Sym-NCO is a regularizer-based training scheme that exploits universal symmetricities in CO problems and solutions.
result Sym-NCO significantly improves DRL-NCO performance across various CO tasks.
We follow the approach employed by Y. Choquet-Bruhat, J. Isenberg and D. Pollack in the case of closed manifolds and establish existence and non-existence results for the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds.
New principles for collapsing law-invariant functionals to means, extending beyond convexity.
problem Conditions for law-invariant functionals to reduce to means.
method Establishing collapse to the mean principles for non-convex functionals.
result General principles apply beyond convexity, including quasiconvex and Choquet integrals.
Transformers improve solving mixed-integer programs, especially CLSP.
problem Solving Capacitated Lot Sizing Problem (CLSP) with mixed-integer programming.
method Employing transformer models to predict binary variables in CLSP.
result Transformer model outperforms CPLEX and LSTM in solving CLSP.
The paper bounds solutions to complex optimization problems with uncertain data.
problem Distributionally robust optimization problems with multivariate uncertainty sets.
method Conditions and bounds derived for multivariate and univariate Wasserstein distances, Bregman-Wasserstein divergences, and signed Choquet integrals.
result Computable lower and upper bounds for DRO problems, derived from scalar-valued aggregation functions and Wasserstein distances.
The paper solves an insurance problem using mean-variance and rank-dependent utility theory.
problem Formulating and solving an insurance problem with rank-dependent utility and mean-variance premium principle.
method Formulated as a non-concave maximization problem, then turned into a concave quantile optimization problem, solved using calculus of variations.
result An optimal insurance contract is derived and numerically computed.
A new convex loss function optimizes set predictions with balanced size and coverage.
problem Optimizing set predictions with balanced size and coverage.
method Proposes a convex loss function using Choquet integrals for nondecreasing subset-valued functions.
result Optimal trade-offs between conditional probabilistic coverage and set size.
New insights into risk aversion for complex decision models.
problem Understanding risk aversion in non-monotone decision models.
method Characterization of probabilistic risk aversion for generalized rank-dependent functions.
result Probabilistic risk aversion is determined by the distortion function, which is convex or scaled quantile-spread mixtures.
Study proves a tight lower bound for MNL-Bandit assortment selection problems.
problem Dynamic assortment planning under MNL bandit model with capacity constraints.
method Proved a tight lower bound on accumulated regret for all parameters.
result Tight lower bound matches existing upper bounds up to logarithmic factors.
Novel spectral embedding considers node weights for graph analysis.
problem Graph node importance quantification.
method Normalized Laplacian eigenvectors for low-energy configurations.
result Weighted embeddings improve graph configurations.
The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved that if the Cauchy problem has a local solution, this solution has a unique maximal…
The paper explores optimal insurance contracts using various deviation measures.
problem Optimal insurance contracts with mean-deviation measures.
method Study of convex signed Choquet integrals and standard deviation as deviation measures, analyzing premium principles like expected value, Value-at-Risk, and Expected Shortfall.
result Characterization of optimal indemnities and deductibles under different premium principles.
Researchers analyze betting odds and free coupons to find exploitable gains.
problem Determining if customers can exploit free coupons for guaranteed gains.
method Using desirability theory and the Choquet integral, they evaluate odds and free coupons.
result Customers can exploit free coupons for guaranteed gains under certain conditions.
In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. When evaluating and comparing competing forecasts, it is then critical that the scoring function used for these purposes be co…
New method ranks European countries' innovation performance considering criterion interactions.
problem Lack of consensus on weighting composite innovation indicators.
method Hierarchical-SMAA-Choquet integral approach to rank and benchmark innovation performance.
result Robust measurement of innovation performances in Europe with a hierarchy of interacting composite indicators.
We prove short-time existence for the Einstein-Euler-Entropy system for non-isentropic fluids with data in uniformly local Sobolev spaces. The cases of compact as well as non-compact Cauchy surfaces are covered. The method employed uses a Lagrangian description of the fluid flow which is based on techniques developed b…
In 1969, Choquet-Bruhat and Geroch established the existence of a unique maximal globally hyperbolic Cauchy development of given initial data for the Einstein equations. Their proof, however, has the unsatisfactory feature that it relies crucially on the axiom of choice in the form of Zorn's lemma. In this paper we pre…
This paper examines various definitions of adversarial risk and their implications.
problem Quantifying the performance of classifiers under adversarial perturbations.
method Optimal transport, robust statistics, functional analysis, and game theory.
result Generalization of Strassen's theorem and new connections to Choquet capacities and game theory.
The paper finds optimal insurance contracts in behavioral finance, avoiding moral hazard.
problem Finding optimal insurance contracts that avoid moral hazard in a behavioral finance framework.
method Formulated as a non-concave maximization problem involving Choquet expectation, then solved using calculus of variations.
result Optimal contracts are found for certain values of safety loading, with some contracts never optimal for others.