This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta pricing relation in place of the market. Thus the difference between the arbitrag…
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48 results for “continuity argument”
Unique solutions found for Plateau problems in smooth and continuous calibrations.
problem Finding unique solutions to the Plateau problem for specific types of currents.
method Boundary regularity theory for area-minimizing currents and unique continuation argument.
result Every compactly supported smoothly or continuously calibrated integral current is the unique solution to the Plateau problem for its boundary data.
Paper proves existence of knot solutions for specific equations.
problem Existence of knot solutions for twisted Kapustin-Witten equations.
method Explicit solutions for t=1, continuity argument in t.
result Proves existence of model knot solutions for any twisting parameter.
This is a continuation of our first paper in [WY16]. There are two purposes of this paper: One is to give a proof of the main result in [WY16] without going through the argument depending on numerical effectiveness. The other one is to provide a proof of our conjecture, mentioned in [TY], where the assumption of negati…
This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for…
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging argumen…
Estimates curvature for long-time continuity method solutions.
problem Curvature estimates for long-time continuity method solutions.
method Adapting arguments from Kähler-Ricci flow to semi-ample canonical line bundles.
result Derives curvature bounds for product manifolds.
Continuity method proves existence of Mabuchi solitons on Fano manifolds.
problem Existence of Mabuchi solitons on extremal Fano manifolds.
method Continuity method applied to Mabuchi's generalized Kähler-Einstein metrics.
result Analytic proof of Mabuchi soliton existence without minimal model program.
Continuous curves inscribe isosceles trapezoids in complex plane.
problem Proving periodic curves inscribe isosceles trapezoids.
method Lagrangian intersection problem and convergence argument.
result Continuous curves inscribe trapezoids with any similarity type.
Paper proves equivalence of derivatives for maps between Carnot groups.
problem Maps between Carnot groups and their derivatives.
method Elementary proof using Euclidean arguments and mean value estimates.
result Maps preserving horizontal curves are continuously Pansu differentiable.
Extends weak continuity of Yang-Mills connections to a broader class.
problem Weak compactness of -Yang-Mills connections.
method Compensation compactness argument applied to Yang-Mills fields.
result Weak continuity result extended to -Yang-Mills connections.
Constructs finite element spaces for -forms, excluding one subspace.
problem Constructing finite element spaces for -forms.
method Piecewise polynomial finite element spaces for all natural subspaces of -forms, excluding one subspace.
result Recovers known finite element spaces and introduces new ones.
In his paper "On the Schlafli differential equality", J. Milnor conjectured that the volume of n-dimensional hyperbolic and spherical simplices, as a function of the dihedral angles, extends continuously to the closure of the space of allowable angles. A proof of this has recently been given by F. Luo (see math.GT/0412…
We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.
The paper provides approximation guarantees for neural networks trained with gradient flow.
problem Approximating neural networks trained with gradient flow in continuous -norm.
method NTK argument for non-convex second but last layer, under-parametrized regime.
result Gradient flow convergence guarantees for neural networks under Sobolev smoothness assumptions.
New algorithm improves online learning with reduced discretization.
problem Improving adaptive online learning with refined discretization.
method Continuous time approach to online learning, followed by a new discretization argument.
result Optimal regret bound with dependence on gradient variance.
Paper constructs continuous families of topological Morse functions.
problem Existence and deformability of topological Morse functions.
method Simple construction of continuous families of topological Morse functions.
result Gives a construction of continuous families of topological Morse functions.
In this paper, we prove the Lipschitz regularity of continuous harmonic maps from an finite dimensional Alexandrov space to a compact smooth Riemannian manifold. This solves a conjecture of F. H. Lin in \cite{lin97}. The proof extends the argument of Huang-Wang \cite {hua-w10}.
Regulated curves on Banach manifolds with continuous projections and regulated derivatives are studied.
problem Regulated curves on Banach manifolds with continuous projections and regulated derivatives.
method Building a Banach manifold structure on the set of such curves.
result Existence of a 'local addition' on such a manifold for any Banach manifold.
Researchers find the optimal exercise time for American options using a specific type of diffusion process.
problem Finding the optimal time to exercise American options with a time-dependent Ornstein-Uhlenbeck process.
method Optimal stopping problem, probabilistic arguments, non-linear Volterra-type integral equation, Picard iteration algorithm.
result They derive a non-linear Volterra-type integral equation and prove the exercise boundary's Lipschitz continuity and differentiability almost everywhere.
Square-like quadrilaterals inscribed in space curves proven for finite total curvature.
problem Square-peg problem in space curves.
method Local curvature analysis and limiting argument on approximating curves.
result Every embedded curve with finite total curvature has an inscribed square-like quadrilateral.
We provide a general Doob-Meyer decomposition for -supermartingale systems, which does not require any right-continuity on the system. In particular, it generalizes the Doob-Meyer decomposition of Mertens (1972) for classical supermartingales, as well as Peng's (1999) version for right-continuous -supermartingale…
Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizonmath.PR
Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.
problem Optimal stopping problems with finite-time horizon and state-dependent discounting.
method Linear diffusion process, time-homogeneous gain function, fine regularity properties, continuity and strict monotonicity proof.
result Proves continuity and strict monotonicity of the optimal stopping boundary under mild assumptions.
We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin--Tits group of dihedral type, but it fails to extend to braids with 4 strands and more. The proof uses a partition of the Cayley graph …
Under mean curvature flow, a closed, embedded hypersurface becomes singular in finite time. For certain classes of mean-convex mean curvature flows, we show the continuity of the first singular time and the limit set "", with respect to initial data. We employ an Angenent-like neck-pinching argument to…
This paper is devoted to a priori estimates for strictly locally convex radial graphs with prescribed Weingarten curvature and boundary in space forms. By constructing two-step continuity process and applying degree theory arguments, existence results in space forms are established for prescribed Gauss curvature …
The paper studies convergence rates of Tsallis entropic regularization in optimal transport.
problem Optimal transport with regularization.
method Γ-convergence and quantization/shadow arguments.
result Derives convergence rate of Tsallis entropic regularization.
We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corresponding Black--Scholes market considering Lipschitz continuous path-dependent payoffs for both discrete- and continuous-time cases. These results are new also for usual American style option…
Over a closed manifold, we consider the sectorial projection of an elliptic pseudo-differential operator A of positive order with two rays of minimal growth. We show that it depends continuously on A when the space of pseudo-differential operators is equipped with a certain topology which we explicitly describe. Our ma…
We prove the existence of optimal strategies for agents with cumulative prospect theory preferences who trade in a continuous-time illiquid market, transcending known results which pertained only to risk-averse utility maximizers. The arguments exploit an extension of Skorohod's representation theorem for tight sequenc…
In this paper, we continue to study the generalized Ricci flow. We give a criterion on steady gradient Ricci soliton on complete and noncompact Riemannian manifolds that is Ricci-flat, and then introduce a natural flow whose stable points are Ricci-flat metrics. Modifying the argument used by Shi and List, we prove the…
Generalization bounds derived for neural ODEs and deep residual networks.
problem Understanding the generalization capability of neural ODEs and deep residual networks.
method Lipschitz-based argument and analogy with deep residual networks.
result A generalization bound involving the magnitude of weight matrix differences.
When doing representation learning on data that lives on a known non-trivial manifold embedded in high dimensional space, it is natural to desire the encoder to be homeomorphic when restricted to the manifold, so that it is bijective and continuous with a continuous inverse. Using topological arguments, we show that wh…
Discrete Riemann Surfacesmath.CV
We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincaré dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow through to the discrete case, we define the discrete analogs of period matrices, Ri…
The paper explores continuous limits of pentagram maps and their relation to KdV equations.
problem Understanding the continuous limits of pentagram maps and their associated KdV equations.
method Quantum calculus and geometric constructions to derive continuous limits and Lax representations.
result Continuous limits of pentagram maps yield specific KdV equations, providing a geometric interpretation.
We present arguments for the formulation of unified approach to different standard continuous inference methods from partial information. It is claimed that an explicit partition of information into a priori (prior knowledge) and a posteriori information (data) is an important way of standardizing inference approaches …
The paper proves continuity of Morse index for Ricci shrinkers.
problem Lower and upper semi-continuity of the Morse index for gradient Ricci shrinkers.
method Adapting and refining recent arguments on CMC hypersurfaces and polynomially weighted Sobolev spaces, with techniques for non-compact shrinkers.
result Identifies a condition ensuring the Morse index of asymptotically conical shrinkers is bounded below by the f-index of their asymptotic cone.
The paper tightens the regret rate for linear bandit problems.
problem Bayesian regret in linear bandit problems.
method Information-theoretic framework and chaining argument.
result Established a new bound with a tight rate of .
Study on optimal portfolio selection with varying borrowing and saving rates in continuous-time markets.
problem Optimal portfolio selection in markets with different borrowing and saving rates.
method Hamilton-Jacobi-Bellman equation, partial differential equation, verification argument.
result Existence and smoothness of the value function, identification of trading regions and strategies.
In this work we address the problem of argument search. The purpose of argument search is the distillation of pro and contra arguments for requested topics from large text corpora. In previous works, the usual approach is to use a standard search engine to extract text parts which are relevant to the given topic and su…
We show the local wellposedness of biharmonic wave maps with initial data of sufficiently high Sobolev regularity and a blow-up criterion in the sup-norm of the gradient of the solutions. In contrast to the wave maps equation we use a vanishing viscosity argument and an appropriate parabolic regularization in order to …
We determine the sample complexity of pure exploration bandit problems with multiple good answers. We derive a lower bound using a new game equilibrium argument. We show how continuity and convexity properties of single-answer problems ensures that the Track-and-Stop algorithm has asymptotically optimal sample complexi…
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition fulfilled by the corresponding value function and show its first regularity property…
Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this work we consider HMMs in continuous time with both constant and switching volati…
Dense neural networks can't approximate all functions.
problem Approximation capabilities of dense neural networks.
method Model compression approach combining weak regularity lemma and graph neural networks.
result Existence of Lipschitz continuous functions not approximable by dense neural networks.
Two Complementary Perspectives to Continual Learning: Ask Not Only What to Optimize, But Also Howcs.LG
New research suggests continual learning should focus on both optimization objective and optimization trajectory.
problem Even with perfect joint loss approximation, continual learning still suffers from forgetting when starting a new task.
method Proposes focusing on both optimization objective and optimization trajectory, combining replay-approximated joint objectives with gradient projection-based optimization routines.
result Combining replay-approximated joint objectives with gradient projection-based optimization routines did not show clear benefits in initial experiments.
Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrageq-fin.PM
The theory of functionally generated portfolios (FGPs) is an aspect of the continuous-time, continuous-path Stochastic Portfolio Theory of Robert Fernholz. FGPs have been formulated to yield a master equation - a description of their return relative to a passive (buy-and-hold) benchmark portfolio serving as the numérai…
In this paper, the relevance of the Feller conditions in discrete time macro-finance term structure models is investigated. The Feller conditions are usually imposed on a continuous time multivariate square root process to ensure that the roots have nonnegative arguments. For a discrete time approximate model, the Fell…