arXiv research

Efficiently learns Single-Index Models with constant factor approximation.

Study proves upper semicontinuity of index plus nullity for minimal and H-CMC hypersurfaces.

This study compares Markowitz and Single-Index models for Malaysian stocks.

We calculate the alternating number of torus knots with braid index 4 and less. For the lower bound, we use the upsilon-invariant recently introduced by Ozsváth, Stipsicz, and Szabó. For the upper bound, we use a known bound for braid index $3$ and a new bound for braid index $4$. Both bounds coincide, so that we obtai…

We show that the Morse index of every 2k-ended solution of the Allen-Cahn equation in R^2 is >= k-1. This bound is expected to be sharp.

Exchange Traded Funds (ETFs) have been gaining increasing popularity in the investment community as is evidenced by the high growth both in the number of ETFs and their net assets since 2000. As ETFs are in nature similar to index mutual funds, in this paper we examined if this growing demand for ETFs can be explained …

Geometric Brownian motion simulates stock prices for Brazilian small caps index.

Study on minimal surfaces with free boundary in a half-space, improving index estimates.

Characterizes diagrams achieving Morton-Franks-Williams inequality for positive knots and links.

Extends width estimates to family case using index theory.

We prove a conformally invariant estimate for the index of Schrödinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound for the index in terms of its energy which is conformally invariant, and captures th…

In this note we prove that any minimal $2$-torus in $S^4$ has Morse index at least $6$, with equality if and only if it is congruent to the Clifford torus in some great $S^3\subset S^4$.For a minimal $2$-torus in $S^n$ with vanishing Hopf differential, we show that its index is at least $n+3$, and that this estimate is…

DIF extends NF with stochastic discrete latent variables for better density estimation.

It has been conjectured that the algebraic crossing number of a link is uniquely determined in minimal braid representation. This conjecture is true for many classes of knots and links. The Morton-Franks-Williams inequality gives a lower bound for braid index. And sharpness of the inequality on a knot type implies the …

Sharp bounds on weak convergence rate for rough volatility models.

We generalize a method by L. Ambrozio, A. Carlotto, and B. Sharp to study the Morse index of closed f-minimal hypersurfaces isometrically immersed in a general weighted manifold. The technique permits, in particular, to obtain a linear lower bound on the Morse index via the first Betti number for closed f-minimal hyper…

Sharp bounds for charged Hawking mass in electrostatic space-times.

A differential geometric characterization of the braid-index of a link is found. After multiplication by 2pi, it equals the infimum of the sum of total curvature and total absolute torsion over holonomic representatives of the link. Upper and lower bounds for the infimum of total curvature over holonomic representative…

Sharp curvature inequality extends Euclidean isoperimetric inequality to Cartan-Hadamard manifolds.

The paper calculates the index and nullity of Fraser-Sargent surfaces and provides bounds.

The ACS criterion is verified for specific hypersurfaces in unit spheres.

We present some geometric applications, of global character, of the bubbling analysis developed by Buzano and Sharp for closed minimal surfaces, obtaining smooth multiplicity one convergence results under upper bounds on the Morse index and suitable lower bounds on either the genus or the area. For instance, we show th…

The VIX is used to enhance quantitative trading strategies.

Second paper applies Morse index to constrained optimization problems.

The study sharpens local Bernstein estimates for Laplace eigenfunctions on compact manifolds.

New superbridge index calculations for knots with odd edges.

Partial (replication) index tracking is a popular passive investment strategy. It aims to replicate the performance of a given index by constructing a tracking portfolio which contains some constituents of the index. The tracking error optimisation is quadratic and NP-hard when taking the L0 constraint into account so …

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the resu…

Sharp theory of neural network scaling laws for hierarchical targets.

We extend the results given by Colbois, Dryden and El Soufi on the relationships between the eigenvalues of the Laplacian and an extrinsic invariant called intersection index, in two directions. First, we replace this intersection index by invariants of the same nature which are stable under small perturbations. Second…

We prove a sharp estimate on the expected value of the integral of the index of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.

We give asymptotically sharp upper bounds for the Khovanov width and the dealternation number of positive braid links, in terms of their crossing number. The same braid-theoretic technique, combined with Ozsváth, Stipsicz, and Szabó's Upsilon invariant, allows us to determine the exact cobordism distance between torus …

This note gives a short, self-contained, proof of a sharp connection between Gittins indices and Bayesian upper confidence bound algorithms. I consider a Gaussian multi-armed bandit problem with discount factor $γ$. The Gittins index of an arm is shown to equal the $γ$-quantile of the posterior distribution of the arm'…

We propose a novel investment decision strategy (IDS) based on deep learning. The performance of many IDSs is affected by stock similarity. Most existing stock similarity measurements have the problems: (a) The linear nature of many measurements cannot capture nonlinear stock dynamics; (b) The estimation of many simila…

Based on a recent theorem due to the authors, it is shown how the extreme tail dependence between an asset and a factor or index or between two assets can be easily calibrated. Portfolios constructed with stocks with minimal tail dependence with the market exhibit a remarkable degree of decorrelation with the market at…

Study efficient estimation of hidden subspaces in Gaussian Multi-index models.

A RL framework for hedging equity index options with realistic costs.

Study shows survivorship bias inflates returns in India's small-cap index.

Study analyzes stock performance before, during, and after the pandemic.

The study predicts solar flare productivity using magnetic data from SDO/HMI.

New constructions show stable geodesics and figure-eights in convex hypersurfaces.

We consider the semi-classical Dirac operator coupled to a magnetic potential on a large class of manifolds including all metric contact manifolds. We prove a sharp local Weyl law and a bound on its eta invariant. In the absence of a Fourier integral parametrix, the method relies on the use of almost analytic continuat…

AIM models explain deep learning in attention layers, offering solvable insights.

This paper uses alternative data to forecast Japanese real estate performance.

We establish multiplicity results for geometrically distinct contractible closed Reeb orbits of non-degenerate contact forms on a broad class of prequantization bundles. The results hold under certain index requirements on the contact form and are sharp for unit cotangent bundles of CROSS's. In particular, we generaliz…

This paper introduces an intersection theory problem for maps into a smooth manifold equipped with a stratification. We investigate the problem in the special case when the target is the unitary group and the domain is a circle. The first main result is an index theorem that equates a global intersection index with a f…

Investors target specific regions of payoff distributions for portfolio optimization.

Study sharp lower bounds on negative eigenvalues of magnetic Pauli operator.