The paper studies geodesics on a specific group using sub-Finsler norms.
problem Finding optimal paths on a Cartan group with sub-Finsler norms.
method Detailed analysis of extremal trajectories, upper bounds on switchings, and classification of extremals.
result Uniform bounds on the number of pieces in piecewise smooth minimizers.
A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of values from the admissible set. Often, such contracts specify that the holder exert control at a…
Under the optimal withdrawal strategy of a policyholder, the pricing of variable annuities with Guaranteed Minimum Withdrawal Benefit (GMWB) is an optimal stochastic control problem. The surrender feature available in marketed products allows termination of the contract before maturity, making it also an optimal stoppi…
Study of sub-Finsler problem on Cartan group using control theory.
problem Sub-Finsler problem on Cartan group.
method Time-optimal control theory, Pontryagin maximum principle.
result Characterization of extremal curves, description of abnormal and singular arcs, construction of bang-bang flow.
A new approach solves optimal trading with linear costs, simplifying multi-asset problems.
problem Optimal trading with linear transaction costs in multi-asset markets.
method Mean-field approach reducing multi-asset to single-asset problem, incorporating risk aversion.
result Simple approximate solution for Ornstein-Uhlenbeck predictors with maximum position constraints.
Let ( B t ) 0 ≤ t ≤ T (B_t)_{0\leq t\leq T} ( B t ) 0 ≤ t ≤ T be either a Bernoulli random walk or a Brownian motion with drift, and let M t : = max { B s : 0 ≤ s ≤ t } M_t:=\max\{B_s: 0\leq s\leq t\} M t := max { B s : 0 ≤ s ≤ t } , 0 ≤ t ≤ T 0\leq t\leq T 0 ≤ t ≤ T . This paper solves the general optimal prediction problem \sup_{0\leqτ\leq T}\sE[f(M_T-B_τ)], where the supremum is over all stopping times τ τ τ adapted to the natural…
The aim of this paper is to adapt the general multitime maximum principle to a Riemannian setting. More precisely, we intend to study geometric optimal control problems constrained by the metric compatibility evolution PDE system; the evolution ("multitime") variables are the local coordinates on a Riemannian manifold,…
The mathematical problem of the static storage optimisation is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise strategy. We show how the solution depends on different constraint types including carr…
The paper develops a valuation framework for GLWB-LTC contracts with Levy dynamics and stochastic interest rates.
problem Valuation of GLWB-LTC contracts with financial guarantees, longevity protection, and health-contingent LTC payments.
method Coupling a recombining Hull-White trinomial tree with an IMEX finite difference scheme, incorporating a seven-state health model.
result Hybrid tree-IMEX method delivers stable long-maturity prices consistent with simulation benchmarks.
Optimal trading strategy in Proof-of-Stake blockchain using continuous-time control.
problem Finding the optimal balance between stake utility and consumption utility in Proof-of-Stake blockchain.
method Continuous-time control approach, dynamic programming, Hamilton-Jacobi-Bellman (HJB) equations.
result Close-form solutions for linear and convex utility functions, optimal strategies identified.
ExGAN generates realistic extreme samples using GANs and EVT.
problem Generating realistic extreme scenarios for risk management.
method ExGAN combines GANs with EVT to model extreme tails of distributions.
result ExGAN efficiently generates extreme samples with constant time complexity.
Study of regular points in extremal subsets of Alexandrov spaces.
problem Characterizing extremal subsets in Alexandrov spaces.
method Definition and analysis of regular points, properties of neighborhoods, and applications to convergence and fibration structures.
result Regular points have full measure and are dense in extremal subsets, with applications to convergence and fibration structures.
Study on extremals in sub-Lorentzian geometry defined by antinorm.
problem Characterizing extremals in sub-Lorentzian structures.
method Deriving Hamiltonian system and conditions for extremal trajectories.
result Conditions for normal extremal trajectories and properties of abnormal extremals.
Paper evaluates CRPS for extreme event forecasts, finding it unsuitable.
problem Verifying probabilistic forecasts of extreme events is challenging.
method Formal framework using extreme value theory to assess CRPS as a random variable.
result CRPS is unsuitable for extreme event verification.
Study models extreme skew surges along French Atlantic coast.
problem Appropriate modelling of extreme skew surges for coastal risk management.
method Peak-over-threshold framework, multivariate generalized Pareto distribution, extreme regression framework.
result Reconstructed historical skew surge time series at stations with limited data.
Blowups of Kähler manifolds can inherit extremal metrics.
problem Extending extremal metrics to blowups of Kähler manifolds.
method Analyzing the action of a torus on blowups and weighted extremal metrics.
result Blowups of Kähler manifolds can inherit weighted extremal metrics.
New approach to extremal hyperbolic surfaces using NEC groups.
problem Structural description of extremal hyperbolic surfaces.
method Uniformization by NEC groups for surfaces with cusps and/or geodesic boundary.
result Full description of automorphism groups of extremal surfaces.
Paper develops a novel approach to identify clusters of features in multivariate extremes.
problem Understanding the complex structure of multivariate extremes in various fields.
method Optimization-based approach to assess the dependence structure of extremes.
result Estimating clusters of features that best capture the support of extremes.
Deep learning models complex multivariate extremes using geometric shapes.
problem Modeling complex extremal dependencies in high-dimensional data.
method Geometric representation and deep learning for flexible semi-parametric models.
result First approach to modeling limit sets using deep learning for high-dimensional data.
Spectral clustering identifies clusters of multivariate extremes.
problem Analyzing the dependence structure of multivariate extremes.
method Spectral clustering based on a random k k k -nearest neighbor graph. result Spectral clustering can consistently identify clusters of multivariate extremes under certain conditions.
New framework estimates treatment effects in extreme data.
problem Hindered by unavailability of counterfactual outcomes and rarity of extreme data.
method Proposes a new framework based on extreme value theory.
result Quantifies treatment effects using tail decay rates of potential outcomes.
Let X X X be a compact Riemann surface of genus ≥ 2 \geq 2 ≥ 2 of constant negative curvature -1. An extremal disk is an embedded (resp. covering) disk of maximal (resp. minimal) radius. A surface containing an extremal disk is an {\em extremal surface}. This paper gives formulas enumerating extremal surfaces of genus ≥ 4 \geq 4 ≥ 4 …
Framework for Granger causality in extreme events.
problem Identifying causal links from extreme events in time series.
method Causal tail coefficient and novel inference method.
result Framework outperforms state-of-the-art methods in detecting Granger causality in extremes.
Model predicts unseen climate extremes to inform risk planning.
problem Missing unseen climate extremes in historical records.
method DeepX-GAN model capturing spatial dependence.
result Unseen heat extremes disproportionately threaten vulnerable regions.
Study on extremal subsets in geodesically complete spaces with curvature constraints.
problem Characterizing extremal subsets in GCBA spaces.
method Introduced and analyzed extremal subsets in GCBA spaces, proving their properties.
result Set of topological singularities forms an extremal subset under additional assumptions.
PCA simplifies multivariate extreme data analysis.
problem Analyzing multivariate extreme values with high-dimensional data.
method Principal Component Analysis (PCA) for dimensionality reduction.
result PCA helps preserve essential information for extreme value analysis.
Extends extreme value mixture models to identify changepoints in financial extreme regimes.
problem Inference over financial extreme regimes is affected by threshold choice.
method Extends extreme value mixture models to account for distributional extreme changepoints using MCMC algorithms.
result Inclusion of different extreme regimes improves financial applications compared to static and dynamic approaches.
Combines GANs and EVT for better modeling of spatial climate extremes.
problem Modeling dependencies between climate extremes, especially in high-dimensional spaces.
method Generative Adversarial Networks (GANs) combined with Extreme Value Theory (EVT).
result evtGAN outperforms classical GANs and statistical approaches in modeling spatial extremes.
Study axisymmetric waves on extremal Kerr spacetime using physical-space estimates.
problem Obtain integrated local energy decay estimates for axisymmetric waves on extremal Kerr backgrounds.
method Use physical-space analysis and a method introduced by Stogin, simplifying Aretakis' derivation.
result Extend Morawetz estimates to extremal Kerr spacetime using purely classical currents.
Extremal metrics exist if uniformly K K K -stable over models.
problem Existence of extremal metrics on complex projective varieties.
method Uniform K K K -stability over models of extremal tori. result Extremal metrics exist if uniformly K K K -stable. Kernel PCA helps analyze multivariate extremes and clusters them effectively.
problem Analyzing the dependence structure of multivariate extremes.
method Kernel PCA as a method for clustering and dimension reduction.
result Kernel PCA preimages effectively identify clusters in multivariate extremes.
Study examines dependence of extreme electricity prices in Australian markets.
problem Understanding and managing risks of extreme price outcomes in Australian electricity markets.
method Examined extremal dependence using extremograms for 5-minute and 30-minute price data.
result Persistence and dependence of extreme prices are influenced by market structure and renewable energy share.
New extremal metrics found on Kähler manifolds.
problem Constructing extremal metrics on Kähler manifolds.
method Test configurations for strictly semistable Kähler manifolds.
result Infinitely many new examples of manifolds with extremal Kähler metrics.
Uniqueness of weighted extremal metrics on Kähler manifolds proven.
problem Uniqueness of weighted extremal Kähler metrics on compact Kähler manifolds.
method Proof of uniqueness using modified Mabuchi energy and weighted K-semistability.
result Uniqueness of weighted extremal Kähler metrics up to automorphisms.
Paper improves risk estimation for extreme events.
problem Estimating extreme risks accurately.
method Modified Bayes risk for expectiles, asymptotic expansions, efficient estimators.
result Asymptotic normality of estimators proved.
A new method reduces uncertainty in predicting rare extreme events without assuming their presence in training data.
problem Predicting rare and extreme events in complex systems with high uncertainty.
method Extreme Event Aware (e2a or η) learning, which enforces extreme event statistics during training.
result Models generate unprecedented extreme events even when training data lacks extremes.
Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with modeling extreme value dependence when that dependence is changing over time, o…
Stability of weighted extremal manifolds proven through blowups.
problem Stability of weighted extremal manifolds.
method Blowup technique to analyze weighted extremal Kähler manifolds.
result Proves weighted extremal manifolds are relatively weighted K-polystable.
New method estimates root-directed tree from extreme data.
problem Discovering causality in river networks from extreme flow data.
method Qualitative max-linear Bayesian network approach to estimate bivariate scores and root-directed spanning tree.
result The new estimator is consistent under max-linear Bayesian network model with noise.
The study finds no extremal metrics for eigenvalues on compact manifolds but constructs examples for annuli.
problem Finding extremal metrics for eigenvalues on compact manifolds.
method Construction of conformally extremal metrics in annuli and analysis of non-existence.
result Construction of conformally extremal metrics in annuli and characterization of these metrics.
Extremal Kähler submanifolds of complex projective spaces have natural extensions.
problem Understanding the structure and properties of extremal Kähler submanifolds.
method Analyzing the natural extensions and holomorphic isometric immersions of extremal Kähler submanifolds.
result Every connected extremal Kähler submanifold has a natural extension which is a complete Kähler manifold.
Extremal length is an important conformal invariant on Riemann surface. It is closely related to the geometry of Teichmuller metric on Teichmuller space. By identifying extremal length functions with energy of harmonic maps from Riemann surfaces to R \mathbb{R} R -trees, we study the second variation of extremal length fu…
Estimates treatment effects in rare extreme events using EVT.
problem Estimating treatment effects in rare, impactful events like extreme climate events.
method Introduces a novel framework using EVT and multivariate regular variation for consistent treatment effect estimation.
result Developed a consistent estimator for extreme treatment effects with rigorous non-asymptotic analysis.
Flexible XVAE model for efficient spatial extremes simulation.
problem Complex tail dependence structures in spatial extremes processes.
method Variational autoencoder (XVAE) for modeling flexible and non-stationary dependence.
result XVAE provides fast inference and outperforms traditional models in high dimensions.
Proves minimization for Kähler manifolds with automorphisms.
problem Minimizing CM degree for Kähler manifolds with automorphisms.
method Equivariant CM minimization conjecture, asymptotic filtration Chow stability.
result Strict minimization by extremal filling.
Extremal length systole is maximized at the Bolza surface.
problem Finding the surface with the maximum extremal length systole.
method Analyzing the Bolza surface and comparing its extremal length systole to others.
result The extremal length systole of the Bolza surface is 2 \sqrt{2} 2 and is a strict local maximum. Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are predictable on the short term. Examining a range of different types of returns and th…
The paper classifies rotationally symmetric extremal Kähler metrics on complex manifolds.
problem Classifying extremal Kähler metrics on complex manifolds.
method Analyzing polynomial zeros in Calabi's extremal equation.
result No U ( n ) U(n) U ( n ) invariant complete extremal Kähler metrics on C n \mathbb C^n C n with positive bisectional curvature.