Contractible Vietoris-Rips complexes for integer n proved using discrete Morse theory.
problem Proving contractibility of Vietoris-Rips complexes for Zn. method Used Bestvina-Brady discrete Morse theory to provide a short and improved proof.
result Contractible Vietoris-Rips complexes at large scales for Zn. Fair insurance contracts are designed to handle default risk using cooperative game theory.
problem Designing fair insurance contracts in the presence of default risk.
method Cooperative game theory to specify premiums and participation in benefit.
result Fair benefit participation emerges as a game outcome involving residual risks.
We survey some topics in A1-homotopy theory. Our main goal is to highlight the interplay between A1-homotopy theory and affine algebraic geometry, focusing on the varieties that are "contractible" from various standpoints.
Optimal contracts help principals delegate data collection in decentralized ML.
problem Dealing with information asymmetries in decentralized ML.
method Design of optimal and near-optimal contracts addressing uncertainty in model quality and performance.
result Simple linear contracts achieve 1-1/e fraction of optimal utility.
The paper analyzes game theory in convertible contracts during liquidity events.
problem Optimizing payments in convertible contracts during liquidity events.
method Defined a general model for games, showed non-existence of pure strategy Nash equilibria, developed algorithms for computing equilibria.
result Optimum pure strategy Nash equilibria exist when all contracts are of the same type (SAFE).
The paper develops a theory of conformal density at infinity for groups with contracting elements.
problem Understanding conformal dynamics at infinity for groups with contracting elements.
method Introducing a class of convergence boundary and establishing the basic theory of conformal density on it.
result Unified theory of conformal density on various boundaries for different types of groups.
We prove the existence of infinitely many periodic points of symplectomorphisms isotopic to the identity if they admit at least one (non-contractible) hyperbolic periodic orbit and satisfy some condition on its flux. The obtained periodic points correspond to periodic orbits whose free homotopy classes are formed by it…
Combines option pricing and portfolio theory for optimal hedging.
problem Optimal hedging of European options in various price dynamics.
method Derives optimal holdings and unhedged risk for different price dynamics.
result Derives solutions for various price dynamics including binomial, diffusion, volatility, volatility-of-volatility, and jump diffusion.
In this paper, we analyse some equity-linked contracts that are related to drawdown and drawup events based on assets governed by a geometric spectrally negative Lévy process. Drawdown and drawup refer to the differences between the historical maximum and minimum of the asset price and its current value, respectively. …
We propose a general notion of algebraic gauge theory obtained via extracting the main properties of classical gauge theory. Building on a recent work on transferring curved A∞-structures we show that, under certain technical conditions, algebraic gauge theories can be transferred along chain contractions. Sp…
Develops theory of relatively Anosov representations using flow examples.
problem Understanding relatively Anosov representations.
method Uses a contracting flow on a bundle to define Anosov representations and builds examples.
result Builds families of examples of relatively Anosov representations.
The problem of equivariant rigidity is the Γ-homeomorphism classification of Γ-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of Γ. In other words, this is the classification of cocompact EfinΓ-manifolds. We use surgery theory, algebraic K-theory, and t…
Proposes a probabilistic framework for smart contract risk quantification.
problem Quantifying financial risk of smart contract cyber attacks and failures.
method Probabilistic graph-theoretical framework using bond percolation models.
result Analytical results and numerical examples for aggregate loss distribution.
LDP is equivalent to contraction of E_γ-divergence, impacting privacy and utility.
problem Analyzing trade-offs between privacy and utility in estimation problems.
method Equivalence of LDP constraints to contraction coefficients of E_γ-divergence, using f-divergences and estimation-theoretic tools.
result LDP guarantees can be expressed in terms of contraction coefficients of arbitrary f-divergences.
This paper investigates Pareto optimal (PO, for short) insurance contracts in a behavioral finance framework, in which the insured evaluates contracts by the rank-dependent utility (RDU) theory and the insurer by the expected value premium principle. The incentive compatibility constraint is taken into account, so the …
In this paper, we use Chas-Sullivan theory on loop homology and Leray-Serre spectral sequence to investigate the topological structure of the non-contractible component of the free loop space on the real projective spaces with odd dimensions. Then we apply the result to get the resonance identity of non-contractible ho…
Theory integrates loss aversion into expected utility for monetary returns.
problem Modeling loss aversion in expected utility theory.
method Develops state-dependent linear utility functions incorporating loss aversion.
result Contracts from monopolists in insurance markets.
Study variance-reduced method for estimating fixed points in Banach spaces.
problem Estimating fixed points of contractive operators in Banach spaces with noisy evaluations.
method Variance-reduced stochastic approximation scheme in Banach spaces.
result Establish non-asymptotic bounds for operator defect and estimation error.
In principal-agent models, a principal offers a contract to an agent to perform a certain task. The agent exerts a level of effort that maximizes her utility. The principal is oblivious to the agent's chosen level of effort, and conditions her wage only on possible outcomes. In this work, we consider a model in which t…
New stability theory for Sinkhorn semigroups with explicit decay rates.
problem Stability and convergence of Sinkhorn iterations for various divergences.
method Operator-theoretic framework based on Lyapunov techniques.
result Explicit exponential decay rates for Sinkhorn iterates.
This paper explores how insurance contracts can be traded in financial markets.
problem The exclusion of arbitrage in insurance contracts due to their non-tradability.
method Defining strategies on insurance portfolios and combining them with financial trading strategies.
result The existence of an insurance-finance-consistent probability, leading to the expected discounted cash-flows.
The paper proves scalar curvature decay for uniformly contractible manifolds with finite asymptotic dimension.
problem Proving decay of scalar curvature for uniformly contractible manifolds with finite asymptotic dimension.
method Using index pairing between Dirac operators and compactly supported vector bundles with Lipschitz control, and Lipschitz control for topological K-theory of finite dimensional simplicial complexes.
result The scalar curvature decays to zero at a rate depending only on the contractibility radius and the diameter control of the asymptotic dimension.
In this paper we consider some insurance policies related to drawdown and drawup events of log-returns for an underlying asset modeled by a spectrally negative geometric Lévy process. We consider four contracts, three of which were introduced in Zhang et al. (2013) for a geometric Brownian motion. The first one is an i…
Gabai showed that the Whitehead manifold is the union of two submanifolds each of which is homeomorphic to R3 and whose intersection is again homeomorphic to R3. Using a family of generalizations of the Whitehead Link, we show that there are uncountably many contractible 3-manifolds with this doub…
Researchers prove spaces of positive scalar curvature metrics are contractible with symmetry.
problem Contractibility of spaces of invariant positive scalar curvature metrics.
method Combining equivariant Morse theory with conformal deformations and local flexibility properties.
result Spaces of invariant positive scalar curvature metrics are contractible.
Analyzes complex structure deformations using cohomology contraction methods.
problem Deforming complex structures and identifying obstructions.
method Refined power series method for (p,q)-forms and complex structures, using Frölicher spectral sequence. result All obstruction classes lie in the kernel of contraction maps under natural vanishing conditions.
The paper shows how contracting elements in groups lead to large quotients with specific growth rates.
problem Understanding the growth rates of group actions with contracting elements.
method Using extension lemma, rotating families theory, and quasi-tree construction.
result There exist sequences of quotient groups with growth rates approaching the original group's growth rate.
We consider a contracting problem in which a principal hires an agent to manage a risky project. When the agent chooses volatility components of the output process and the principal observes the output continuously, the principal can compute the quadratic variation of the output, but not the individual components. This…
Study loan contracts in DLPs using derivatives pricing and neural networks.
problem Optimizing and hedging risks in decentralized lending contracts.
method Derivatives pricing theory, deep neural networks, and statistical arbitrage.
result Developed a method to hedge risks in lending contracts and exploit arbitrage opportunities.
Bayesian posterior contraction rates improve with decreasing tails
problem Bayesian posterior contraction in nonparametric settings
method Using p-exponential tails for contraction rates result Improvement in contraction rates with decreasing tails
In this paper, we prove that for every irreversible Finsler n-dimensional real projective space (RPn,F) with reversibility λ and flag curvature K satisfying 916(1+λλ)2<K≤1 with λ<3, there exist at least n−1 non-contractible closed geodesics. In addition, if the met…
We will show that for a polynomially contractible manifold of bounded geometry and of polynomial volume growth every coarse and rough cohomology class pairs continuously with the K-theory of the uniform Roe algebra. As an application we will discuss non-vanishing of rough index classes of Dirac operators over such mani…
We study Eγ-divergence contraction and its privacy implications.
problem Analyzing privacy in data processing and algorithms.
method Generalizing Dobrushin's coefficient to Eγ-divergence and deriving contraction coefficients. result Local differential privacy can be expressed in terms of Eγ-divergence contraction, leading to precise sample size reductions. Sharp growth tightness proven for group quotients.
problem Growth behavior of group quotients by confined subgroups.
method Statistically convex-cocompact action with contracting elements.
result Sharp growth tightness proven, with applications to uniformly recurrent subgroups.
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.
This paper extends Lie algebra contractions to infinite-dimensional spaces for better understanding of group limits.
problem Understanding group limits through Lie algebra contractions, especially in infinite-dimensional settings.
method Using infinite-dimensional Lie algebras and their integration theory, the paper constructs Lie group expansions.
result Explicit descriptions of Lie groups in elementary terms, including applications to Newtonian gravity.
PL Morse theory proves strong regularity in low dimensions.
problem Understanding regular and critical points in PL manifolds.
method Introducing homologically and strongly regular points, presenting criteria, and constructing examples.
result In low dimensions d≤4, homologically regular points are always strongly regular. There are two natural simplicial complexes associated to the noncrossing partition lattice: the order complex of the full lattice and the order complex of the lattice with its bounding elements removed. The latter is a complex that we call the noncrossing partition link because it is the link of an edge in the former. …
The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert's projective metric or to a related family of seminorms (Hopf's oscillation or Hilbert's seminorm). We generalize these properties to abstract consensus operators over normal cones, w…
In the paper [Probab. Theory Relat. Fields, 100 (1994) 417-428] Xue-Mei Li has shown that the moment stability of an SDE is closely connected with the topology of the underlying manifold. In particular, she gave sufficient condition on SDE on a manifold M under which the fundamental group π1M=0. We prove that in …
The paper analyzes reinsurance strategies in peer-to-peer insurance schemes.
problem Strategic interaction between plan managers and reinsurers in P2P insurance.
method Develops two game-theoretic contract designs: Pareto and Bowley designs, deriving optimal contracts and analyzing their welfare effects.
result The Bowley design yields a unique optimal contract, while the Pareto design allows for multiple Pareto-optimal contracts.
Bayesian nonparametric models get better posterior estimates via SPDE methods.
problem Estimating posterior distributions in nonparametric Bayesian models.
method Extending diffusion methods to SPDEs on Hilbert spaces for posterior contraction and Laplace approximation.
result Derivation of posterior contraction rates and finite-sample Bernstein von Mises results.
We prove contractibility of VR complexes for integer lattices up to dimension 5.
problem Contractibility of Vietoris-Rips complexes for integer lattices.
method Analyzing the homotopy type and contractibility of VR complexes for integer lattices.
result Contractibility of VR complexes for integer lattices up to dimension 5.
Study random walks on CAT(0) spaces with contracting elements, proving limit laws.
problem Analyzing random walks on spaces with non-positive curvature.
method Use of contracting elements and hyperbolic models for CAT(0) spaces.
result Prove almost sure convergence to the boundary without moment assumption.
Bayesian analysis shows unlabeled data improve graph-based semi-supervised learning.
problem Improving semi-supervised learning with limited labeled data.
method Bayesian nonparametric approach using unlabeled data for graph-based learning.
result Posterior contracts optimally around the truth with sufficient unlabeled data.
We investigate families of Legendrian submanifolds of 1-jet spaces by developing and applying a theory of families of generating family homologies. This theory allows us to detect an infinite family of loops of Legendrian n-spheres embedded in the standard contact (2n+1)-space (for n>1) that are contractible in the smo…
The present work studies and analyzes general defaultable OTC contract in presence of a contingent CSA, which is a theoretical counterparty risk mitigation mechanism of switching type that allows the counterparty of a general OTC contract to switch from zero to full/perfect collateralization and switch back whenever sh…
The paper explores coalescent contractions in contractible spaces, providing criteria and examples.
problem Existence and absence of coalescent contractions in contractible spaces.
method Analysis of contractible finite simplicial complexes and criteria for coalescent contractions.
result Criteria for contractible finite simplicial complexes that ensure no coalescent contractions.