Study inert and ambiguous classes in modular group using combinatorial methods.
problem Counting inert and ambiguous conjugacy classes in modular group.
method Purely combinatorial approach using word length in free product representation.
result Exact counting formulas and asymptotic growth rates for inert and ambiguous classes.
Study nonconcave portfolio choice with smooth ambiguity and Bayesian learning.
problem Nonconcave portfolio choice under smooth ambiguity and Bayesian learning.
method Developed a general framework for dynamic, non-concave asset allocation.
result Dynamic consistency achieved through a robust representation.
ITCA optimizes label combination for ambiguous outcomes in multi-class classification.
problem Ambiguous outcome labels in real-world datasets hinder accurate multi-class classification.
method Information-theoretic classification accuracy (ITCA) and search strategies (greedy, breadth-first) guide label combination.
result ITCA improves prediction accuracy and identifies ambiguous labels across diverse applications.
Investment strategy in ambiguous financial markets with learning
problem Continuous time investment problem in multi-asset Black-Scholes market with model ambiguity
method Optimal dynamic investment strategy within the class of all adapted strategies which allow for learning
result Ambiguity averse investors invest less in risky assets
We investigate the impact of Knightian uncertainty on the optimal timing policy of an ambiguity averse decision maker in the case where the underlying factor dynamics follow a multidimensional Brownian motion and the exercise payoff depends on either a linear combination of the factors or the radial part of the driving…
We consider the impact of ambiguity on the optimal timing of a class of two-dimensional integral option contracts when the exercise payoff is a positively homogeneous measurable function. Hence, the considered class of exercise payoffs includes discontinuous functions as well. We identify a parameterized family of exce…
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.
A firm with heterogeneous shareholders optimizes dividends under ambiguity aggregation.
problem Optimizing dividends for a firm with heterogeneous shareholders under ambiguity aggregation.
method Characterizing equilibrium dividends using a partition of the state space.
result Time-homogeneous equilibrium dividend law characterized by a partition of the state space.
The paper uses EVT to improve tail risk measures under ambiguity sets.
problem Misspecification of tail risk measures leads to inflated risk estimates.
method Applies Extreme Value Theory to derive worst-case tail risk under ambiguity sets.
result Proposes a tail-calibrated ambiguity design that preserves nominal tail asymptotic scaling.
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.
The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of the two classes, while the overlap is an ambiguity region which could belong to e…
Unified framework for set-valued classification tackles ambiguous multi-class datasets.
problem Ambiguous multi-class datasets in modern statistics.
method Unified statistical framework encompassing various set-valued classification formulations.
result Infinite sample optimal strategies and plug-in principle for data-driven algorithms.
Study optimizes insurance and investment strategies for risk-averse insurers under ambiguity.
problem Optimizing insurance and investment strategies for risk-averse insurers under ambiguity.
method Solves a coupled FBSDE to derive optimal strategies and value function.
result Optimal consumption, investment, and reinsurance strategies influenced by risk aversion and EIS.
Paper proposes online optimization for uncertain systems using machine learning and DRO.
problem Optimization of uncertain dynamical systems with distributional uncertainty.
method Combines machine learning with Distributional Robust Optimization (DRO) to handle uncertainty.
result Online solutions with probabilistic regret bounds for uncertain systems.
Paper resolves ambiguity in non-convex bilevel optimization problems.
problem Ambiguity in bilevel optimization with non-convex lower-level objectives.
method Introduces selection maps to define critical points and resolves ambiguity.
result Validates new analytical tools in Morse theory for implicit differentiation.
New method for finding optimal treatment regimes in medical settings with time-varying unobserved factors.
problem Finding optimal treatment regimes in medical settings with time-varying unobserved factors.
method Extend Dynamic Treatment Regimes (DTRs) to Ambiguous Dynamic Treatment Regimes (ADTRs), connect to Ambiguous Partially Observable Mark Decision Processes (APOMDPs), and develop Reinforcement Learning methods.
result Established theoretical results for learning methods, including consistency and asymptotic normality.
In most classification tasks there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classifiers output sets of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framewo…
Investment strategy optimized for ambiguity and interest rate risk.
problem Dynamic asset allocation with interest rate risk and ambiguity.
method Closed-form solution for optimal investment strategy.
result Ambiguity affects speculative motives, not hedging of interest rate risk.
Quantum computing speeds up asset pricing models exponentially.
problem Solving dynamic nonlinear asset pricing models efficiently.
method Utilizes quantum superposition and entanglement to solve models exponentially faster than classical methods.
result Exponential computational speed-up for solving asset pricing models.
This paper examines how data affects risk measures in uncertain distributions.
problem How does distributional ambiguity affect risk measures?
method Formulated and derived simpler dual problems for infinite and finite dimensional robust moment problems.
result Developed theory and conducted experiments in inventory control and portfolio management.
In this paper, we study optimal switching problems under ambiguity. To characterize the optimal switching under ambiguity in the finite horizon, we use multidimensional reflected backward stochastic differential equations (multidimensional RBSDEs) and show that a value function of the optimal switching under ambiguity …
Study insurance pricing under correlation ambiguity without increasing prices or reducing utility.
problem Understanding the dependence structure between insurance and financial risks.
method Dynamic equilibrium analysis of insurance pricing with worst-case beliefs.
result Correlation ambiguity does not necessarily increase insurance prices or reduce insurers' utility.
New formulations capture aversion to ambiguity about volatility.
problem Capturing aversion to ambiguity about unknown and time-varying volatility.
method Introduces novel preference formulations and compares them with existing models.
result Illustrates the impact of ambiguity aversion in static and dynamic models.
A framework for robust exploration in reinforcement learning under ambiguity.
problem Optimal stopping under ambiguity in reinforcement learning.
method Continuous-time robust reinforcement learning framework using g-expectation and backward stochastic differential equations. result Constructs a robust exploratory stopping time approximating the optimal stopping time under ambiguity.
Study improves adversarial classification using distributionally robust models.
problem Improving robustness against adversarial attacks in classification models.
method Distributionally robust chance constraints with Wasserstein ambiguity, reformulated as a regularized ramp loss minimization problem.
result Standard descent methods can converge to the global minimizer for the distributionally robust adversarial classification model.
Improves classifier accuracy in ambiguous data settings.
problem Training classifiers with partially labeled data.
method Incremental pruning of candidate labels using conformal prediction.
result Significantly improves test set accuracies of PLL classifiers.
We study the dynamic indifference pricing with ambiguity preferences. For this, we introduce the dynamic expected utility with ambiguity via the nonlinear expectation--G-expectation, introduced by Peng (2007). We also study the risk aversion and certainty equivalent for the agents with ambiguity. We obtain the dynamic …
Model cash management under ambiguity using maxmin preferences and diffusion.
problem Optimizing cash reserves in the presence of ambiguity.
method Singular control model with maxmin preferences, verified using Dynkin games.
result Higher expected costs and narrower inaction region under increased ambiguity.
Paper investigates Lambda Value-at-Risk under ambiguity and risk sharing.
problem Investigates Lambda Value-at-Risk under ambiguity and risk sharing.
method Establishes equivalence of robust ΛVaR and traditional ΛVaR under ambiguity sets, analyzes properties, derives explicit formulas, and explores risk sharing. result Unified and extended the concept of Value-at-Risk under ambiguity, derived explicit formulas for specific ambiguity sets, and explored risk sharing.
In this note we prove that equivariantly homeomorphic quasitoric manifolds are diffeomorphic. As a consequence we show that up to finite ambiguity the diffeomorphism type of certain quasitoric manifolds M is determined by their cohomology rings and first Pontrjagin classes.
The paper explores continuous inverse ambiguous functions on various Lie groups.
problem Existence of continuous inverse ambiguous functions on Lie groups.
method Investigation of continuous inverse ambiguous functions on specific Lie groups.
result Existence of continuous inverse ambiguous functions on various Lie groups.
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an α-maxmin nonlinear expectation, renders the stopping problem time-inconsistent. We look for subgame perfect…
A geometric account explains why 'The Dress' is ambiguous, predicting observable signatures in image processing.
problem Understanding and predicting ambiguity in image processing, particularly in intrinsic image decomposition.
method Geometric analysis of intrinsic image decomposition, focusing on the discontinuous switch in prior-mode sections.
result Predicted signatures in albedo Jacobian and Fernet curvature can be observed in various models and datasets.
Improves DRO with Bayesian Ambiguity Sets for model misspecification.
problem Overly conservative decisions due to misspecified models in DRO.
method Introduces DRO-RoBAS with robust posterior predictive distribution.
result Outperforms other Bayesian and empirical DRO approaches in out-of-sample performance.
Study optimal timing to divest from assets with uncertain future scenarios.
problem Optimal timing to divest from assets with uncertain future scenarios.
method Smooth model of decision making under ambiguity aversion, optimal stopping problem with learning.
result Proves a minimax result reducing the problem to standard optimal stopping problems with learning.
Optimal policies in Markov decision processes (MDPs) are very sensitive to model misspecification. This raises serious concerns about deploying them in high-stake domains. Robust MDPs (RMDP) provide a promising framework to mitigate vulnerabilities by computing policies with worst-case guarantees in reinforcement learn…
Ordinal data are often seen in real applications. Regular multicategory classification methods are not designed for this data type and a more proper treatment is needed. We consider a framework of ordinal classification which pools the results from binary classifiers together. An inherent difficulty of this framework i…
This paper compares average-K and top-K classification methods under ambiguity.
problem Choosing a single label in ambiguous cases leads to low precision.
method Formally characterizes ambiguity profiles and compares average-K and top-K classification methods.
result Average-K can achieve lower error rates than top-K in some ambiguous cases.
Proposes handling ambiguity in sequential data predictions.
problem Handling uncertainty in sequential data predictions.
method Extension of MHP model to recurrent architectures, introducing a novel metric.
result Achieved promising results on various sequential data tasks.
This paper compares different DRO formulations for pension fund management.
problem Navigating uncertainty in asset liability management for pension funds.
method Three DRO formulations: mixture, box, and Wasserstein ambiguity sets.
result Wasserstein and box ambiguity sets outperform traditional approaches in fund performance.
Identifying emotion from speech is a non-trivial task pertaining to the ambiguous definition of emotion itself. In this work, we adopt a feature-engineering based approach to tackle the task of speech emotion recognition. Formalizing our problem as a multi-class classification problem, we compare the performance of two…
Robust MDPs (RMDPs) can be used to compute policies with provable worst-case guarantees in reinforcement learning. The quality and robustness of an RMDP solution are determined by the ambiguity set---the set of plausible transition probabilities---which is usually constructed as a multi-dimensional confidence region. E…
Adapts AUM to identify ambiguous tasks in crowdsourced learning, improving generalization.
problem Discerning ambiguous tasks in crowdsourced labels to prevent mislabeling.
method Introduces Weighted Areas Under the Margin (WAUM) to average AUMs weighted by task-specific scores.
result Improves generalization performance by discarding ambiguous tasks.
Recent unsupervised approaches to domain adaptation primarily focus on minimizing the gap between the source and the target domains through refining the feature generator, in order to learn a better alignment between the two domains. This minimization can be achieved via a domain classifier to detect target-domain feat…
Researchers resolved ambiguities in gravitational radiation charges.
problem Ambiguities in charges related to gravitational radiation.
method Addressed supertranslation ambiguities in classical and extended BMS algebras.
result Proposed and proved an invariant charge free from supertranslation ambiguity.
Paper tackles robust control of SDEs with ambiguity, proving value function existence and applying to investment problems.
problem Robust control of SDEs with ambiguity parameters and non-Lipschitz coefficients.
method Existence and uniqueness of value function established through BSDEs with non-linear growth conditions.
result Existence and uniqueness of value function in proper space, verified through BSDEs.
According to conventional wisdom, ambiguity accelerates optimal timing by decreasing the value of waiting in comparison with the unambiguous benchmark case. We study this mechanism in a multidimensional setting and show that in a multifactor model ambiguity does not only influence the rate at which the underlying proce…
Study examines insurance demand under ambiguity aversion.
problem Demand for insurance indemnification under ambiguity aversion.
method Characterizes optimal indemnity functions using Maxmin-Expected Utility model.
result Optimal indemnity functions involve full insurance on low-probability events.