New optimal trading strategies found for risk-averse and cumulative prospect theory traders in illiquid markets.
problem Optimal trading strategies for risk-averse and cumulative prospect theory traders in illiquid markets.
method An extension of Skorohod's representation theorem for tight sequences of probability measures.
result Existence of optimal strategies for agents with cumulative prospect theory preferences in continuous-time illiquid markets.
When estimating the risk of a P&L from historical data or Monte Carlo simulation, the robustness of the estimate is important. We argue here that Hampel's classical notion of qualitative robustness is not suitable for risk measurement and we propose and analyze a refined notion of robustness that applies to tail-depend…
We introduce the concept of singular recursive utility. This leads to a kind of singular BSDE which, to the best of our knowledge, has not been studied before. We show conditions for existence and uniqueness of a solution for this kind of singular BSDE. Furthermore, we analyze the problem of maximizing the singular rec…
The present paper deals with the characterization of no-arbitrage properties of a continuous semimartingale. The first main result, Theorem \refMainTheoremCharNA, extends the no-arbitrage criterion by Levental and Skorohod [Ann. Appl. Probab. 5 (1995) 906-925] from diffusion processes to arbitrary continuous semimartin…
Optimal martingale transport plans without structural assumptions.
problem Finding optimal martingale transport plans.
method Left-monotone martingale coupling and Skorokhod embedding.
result Left-monotone coupling is optimal under specific conditions.
Let (Xt)t≥0 be a continuous-time, time-homogeneous strong Markov process with possible jumps and let τ be its first hitting time of a Borel subset of the state space. Suppose X is sampled at random times and suppose also that X has not hit the Borel set by time t. What is the intensity process of τ ba…
This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions, and we consider a general…
We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). I…
Optimal stopping times maximize/minimize Brownian motion distance between radially symmetric marginals.
problem Optimal stopping times for Brownian motion between radially symmetric marginals.
method Characterization through Skorohod embeddings and optimal mass transport with subharmonic constraints.
result Optimal stopping times are hitting times of suitable barriers, non-randomized, and unique under radial symmetry.
Novel representer theorem for metric and preference learning in RKHSs.
problem Metric and preference learning problems in Hilbert spaces.
method Regularization with respect to task structure norm, RKHS representation, and novel algorithm.
result Significant performance improvement over baseline methods in real-world rank inference benchmarks.
Representer theorem conditions extended to reflexive Banach spaces.
problem Conditions for representer theorem in reflexive Banach spaces.
method Proved necessary and sufficient conditions for representer theorems in reflexive Banach spaces.
result Solution independence of regularizer in reflexive Banach spaces.
Survey of recent Kleinian representation convergence results.
problem Kleinian representation convergence
method Survey and analysis of recent results following Thurston's theorems
result Survey of recent and less recent results on convergence of Kleinian representations
Representer theorem extended to Banach spaces for nondifferentiable regularizers.
problem Conditions for a representer theorem in Banach spaces.
method Generalized representer theorem to Banach spaces for nondifferentiable regularizers.
result Necessary and sufficient conditions for a representer theorem in Banach spaces.
A theorem for Hilbert space-valued functions simplifies machine learning models.
problem Learning functions in Hilbert space-valued spaces.
method Generalized Representer Theorem for Hilbert space-valued functions.
result Unified view of supervised and semi-supervised learning methods.
Study k-positive surface group representations and their degenerations.
problem Understanding the behavior of surface group representations under degenerations.
method Introduced k-positive representations and studied their degenerations using a limit theorem for positively ratioed representations.
result Degenerations of k-positive representations can lead to limits that are at least (k-3)-positive and irreducible limits are (k-1)-positive.
Geometrically, Kostant's Convexity Theorem is extended to submetries with a fat section.
problem Extending Kostant's Convexity Theorem to a broader class of representations.
method Introducing a new concept of 'fat section' and proving the theorem for submetries with this property.
result Kostant's Convexity Theorem is partially extended to submetries with a fat section.
New examples of embeddings defy Anosov representation limits.
problem Examples of robust quasi-isometric embeddings not approximated by Anosov representations.
method Exhibited non-locally rigid, Zariski dense embeddings in SLm(K). result Higher rank Anosov representation theorems fail for m≥30. Study local structure of knot group representations into SL(n,C).
problem Understanding the local structure of knot group representations.
method Analysis of tangent cone and use of Luna's slice theorem.
result Local structure of representation variety at diagonal representations.
New representations defined for groups and graphs, with applications to stable representations.
problem Defining and constructing new types of representations for groups and graphs.
method Introducing (R,Λ)-directed Anosov representations and using Fock-Goncharov positivity to construct them. result Constructs large families of primitive stable representations from F2 to PGL(V), including non-discrete and non-faithful examples. Paper generalizes regularization methods for Banach spaces.
problem Ill-posedness in machine learning and signal reconstruction.
method Generalizes regularization to Banach spaces and presents a representer theorem.
result Retrieves and extends known results in optimization and machine learning.
Graphs improve theorem proving in higher-order logic.
problem Challenges in converting higher-order logic formulas into graph-based representations.
method Used graph neural networks (GNNs) to represent and search higher-order logic.
result GNNs outperform state-of-the-art methods in higher-order theorem proving.
The paper explores Schwartz representations and their connection to Anosov representations.
problem Understanding the relationship between Schwartz representations and Anosov representations of the modular group.
method Constructing families of Anosov representations and analyzing their limits.
result Schwartz representations are limits of Anosov representations of the modular group.
Entropy rigidity theorem for cusped Hitchin representations.
problem Entropy rigidity for Hitchin representations of cusped groups.
method Introduction of (1,1,2)-hypertransverse groups and transverse representations.
result Hausdorff dimension of conical limit set agrees with simple root entropy.
By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group G on a smooth or analytic manifold M with a rigid A-structure σ. It generalizes Gromov's centralizer and representation theorems to the case where R(G) is split solvable and $G/R(G…
We present a new direct proof of a topological representation theorem for oriented matroids in the general rank case. Our proof is based on an earlier rank 3 version. It uses hyperline sequences and the generalized Sch{ö}nflies theorem. As an application, we show that one can read off oriented matroids from arrangement…
We generalize a theorem of Burde and de Rham characterizing the zeros of the Alexander polynomial. Given a representation of a knot group π, we define an extension of π, the Crowell group. For any GL(n,C) representation of π, the zeros of the associated twisted Alexander polynomial correspond to representations o…
Revisits the connection between neural networks and the Kolmogorov-Arnold theorem.
problem Explains the limitations of using the Kolmogorov-Arnold theorem to explain neural networks with multiple hidden layers.
method Derives modifications of the Kolmogorov-Arnold representation that transfer smoothness properties to the outer function and can be well approximated by ReLU networks.
result Shows that a deep neural network with most layers approximating the interior function is a more natural interpretation of the Kolmogorov-Arnold representation.
Nonexistence theorem for product type manifolds, proving no locally conformally flat metrics.
problem Proving nonexistence of locally conformally flat metrics on product manifolds.
method Nonexistence theorem for product type manifolds.
result 4-manifold Σ_g×Σ_h does not admit locally conformally flat metrics for g≥2 and h≥1.
We prove a theorem relating the automorphism group of a Cartan geometry to the group on which the geometry is modeled: a component of the adjoint representation of the first embeds in the adjoint representation of the second. Consequences of the theorem include general bounds on the rank and nilpotence degree of an aut…
The abstract discusses Lie 2-groupoids and their applications in representation theory.
problem Understanding symmetries of graded vector spaces and bundles.
method Construction of Lie 2-groupoids and exploration of their properties.
result Smooth pseudofunctors classify 2-term representations up to homotopy.
The article discusses extensions of Harish-Chandra's admissibility theorem.
problem Restrictions of irreducible representations to non-compact subgroups.
method Representation-theoretic developments for new spectral analysis.
result Powerful methods for spectral analysis of standard locally symmetric spaces.
SL(n) covariant valuations on Orlicz spaces are represented and characterized.
problem Representing SL(n) covariant valuations on Orlicz spaces.
method Representation theorem established for continuous, SL(n) covariant vector-valued valuations.
result Unique characterization of SL(n) covariant valuations as moment vectors.
New examples show embeddings not approximated by Anosov representations.
problem Understanding quasi-isometric embeddings of word hyperbolic groups into SL(d,R). method Constructing specific examples of embeddings that are not limits of Anosov representations.
result Analogous density theorem does not hold for SL(d,R) when d⩾5. New proof of Alesker's Irreducibility Theorem using localization techniques.
problem Representing polynomial valuations on convex bodies.
method Introducing a localization technique for polynomial valuations and reducing to a representation problem for differential forms.
result Smooth and translation invariant valuations are representable by integration with the normal cycle.
Extends Lawrence's representations to integral Uqsl(2) Verma-modules and braid groups.
problem Integrating Lawrence's representations into Uqsl(2) Verma-modules and braid groups. method Defining homological operators and showing they provide a representation for Uqsl(2), establishing isomorphisms and preserving key properties. result Recovering an integral version of Kohno's theorem for Verma-modules and braid group representations.
PARIS reduces imbalanced regression datasets by pruning uninformative samples.
problem Imbalanced regression where models focus on high-frequency regions, ignoring rare but impactful events.
method PARIS uses the representer theorem to compute a closed-form representer deletion residual for iterative pruning of the training set.
result PARIS reduces training set by up to 75% while preserving or improving overall performance, outperforming other methods.
Link groups can only have certain SU(2) representations.
problem Characterizing SU(2) representations of link groups.
method Analyzing the structure of link groups and their representations in SU(2).
result Irreducible SU(2) representations of link groups are restricted to specific configurations.
Proves a generalization of a multiplicity one theorem for specific groups.
problem Generalizing a multiplicity one theorem for spherical representations.
method Analyzes τn-spherical representations of G=SO(2,1)∘. result Proves an analogue of the strong multiplicity one theorem.
The paper provides a spinorial representation for submanifolds in Lie groups.
problem Representation of submanifolds in Lie groups.
method Spinorial representation approach.
result Spinorial proof of the Fundamental Theorem for submanifolds in Lie groups.
Developed algebraic theory of bonded braids, proving Markov theorem.
problem Studied bonded knots and their algebraic properties.
method Introduced bonded braid monoid, proved Alexander and Markov theorems.
result Every bonded knot is the closure of a bonded braid, and equivalent knots have related braid representatives.
Paper proves almost all stabilizer subgroups of Thompson's group satisfy Alexander's theorem.
problem Alexander's theorem for stabilizer subgroups of Thompson's group.
method Defined a method to construct knots and links from Thompson's group F and proved Alexander's theorem for stabilizer subgroups.
result Almost all stabilizer subgroups under the natural action on the unit interval satisfy Alexander's theorem.
Represents neural networks as solutions to inverse problems in Banach spaces.
problem Understanding the function learned by neural networks.
method Variational framework, representer theorem, polynomial ridge splines.
result Neural networks are solutions to inverse problems in Banach spaces.
We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical t…
In this paper we explain how Morse theory for the Yang-Mills functional can be used to prove an analogue, for surface groups, of the Atiyah-Segal theorem. Classically, the Atiyah-Segal theorem relates the representation ring R(Γ) of a compact Lie group Γ to the complex K-theory of the classifying space BΓ. For infi…
Paper generalizes representations of Lie algebroids to weighted Lie algebroids.
problem Representations of Lie algebroids and their generalizations.
method Introducing and studying weighted Lie algebroids, showing relations to VB-algebroids and generalizing the van Est theorem.
result New natural examples of higher term representations up to homotopy of Lie algebroids uncovered.
Paper develops efficient estimator for Hawkes processes using representer theorem.
problem Estimating latent triggering kernels for Hawkes processes from event sequences.
method Penalized least squares minimization in RKHS framework.
result Efficient estimator with competitive accuracy and improved computational efficiency.
The paper proves approximation and interpolation theorems for maxfaces with singularities.
problem Proving approximation and interpolation theorems for maxfaces with singularities.
method Surveying and applying Enneper--Weierstrass representation formula methods to maxfaces, incorporating singularity criteria.
result Existence of maxfaces with prescribed singularities and maxfaces with dense image singular set.
Geometric models for representations up to homotopy using simplicial vector bundles.
problem Geometric models for representations up to homotopy of Lie groupoids.
method Application of higher analogs of cleavages in simplicial fibrations to geometric models.
result An equivalence between representations up to homotopy and simplicial vector bundles endowed with a cleavage.