arXiv research

Contractible Vietoris-Rips complexes for integer n proved using discrete Morse theory.

Fair insurance contracts are designed to handle default risk using cooperative game theory.

We survey some topics in ${\mathbb A}^1$-homotopy theory. Our main goal is to highlight the interplay between ${\mathbb A}^1$-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.

The paper analyzes game theory in convertible contracts during liquidity events.

The paper develops a theory of conformal density at infinity for groups with contracting elements.

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…

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 $A_{\infty}$-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.

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 $E_{fin}Γ$-manifolds. We use surgery theory, algebraic $K$-theory, and t…

In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the contract's maturity the contract is perfectly hedged. We derive both the optimal hol…

Proposes a probabilistic framework for smart contract risk quantification.

LDP is equivalent to contraction of E_γ-divergence, impacting privacy and utility.

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.

Study variance-reduced method for estimating fixed points in Banach spaces.

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.

This paper explores how insurance contracts can be traded in financial markets.

The paper proves scalar curvature decay for uniformly contractible manifolds with finite 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 $\mathbb R^3$ and whose intersection is again homeomorphic to $\mathbb R^3$. 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.

Analyzes complex structure deformations using cohomology contraction methods.

The paper shows how contracting elements in groups lead to large quotients with specific growth rates.

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.

Bayesian posterior contraction rates improve with decreasing tails

In this paper, we prove that for every irreversible Finsler $n$-dimensional real projective space $(\mathbb{R}P^n,F)$ with reversibility $λ$ and flag curvature $K$ satisfying $\frac{16}{9}\left(\fracλ{1+λ}\right)^2<K\le 1$ 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 $E_γ$-divergence contraction and its privacy implications.

Sharp growth tightness proven for group quotients.

The paper solves an insurance problem using mean-variance and rank-dependent utility theory.

This paper extends Lie algebra contractions to infinite-dimensional spaces for better understanding of group limits.

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 $π_1 M=0$. We prove that in …

The paper analyzes reinsurance strategies in peer-to-peer insurance schemes.

Bayesian nonparametric models get better posterior estimates via SPDE methods.

We prove contractibility of VR complexes for integer lattices up to dimension 5.

Study random walks on CAT(0) spaces with contracting elements, proving limit laws.

Bayesian analysis shows unlabeled data improve graph-based semi-supervised learning.

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.

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured…