arXiv research

Paper analyzes multidimensional PIDEs for financial modeling, proving existence and uniqueness in Bessel spaces.

Paper proves existence and uniqueness of solutions to PIDEs in Bessel spaces for option pricing.

Derivatives of sub-Riemannian geodesics are always $L_p$-Hölder continuous.

Global harmonic maps into SU(1,1) constructed from Smyth potentials using DPW method.

This paper extends barrier option pricing to CIR and CEV models using semi-closed form solutions.

It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with singularities and boundary, provided suitable weights, which reflect the nature of the s…

The paper defines function spaces on manifolds with bounded or singular geometries.

A rather complete investigation of anisotropic Bessel potential, Besov, and Hölder spaces on cylinders over (possibly) noncompact Riemannian manifolds with boundary is carried out. The geometry of the underlying manifold near its 'ends' is determined by a singularity function which leads naturally to the study of weigh…

The tetrahedral index connects to a q-Bessel function, revealing new mathematical techniques.

We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale …

Directly simulates squared Bessel processes efficiently.

In this note we construct a family of immersions with constant mean curvature of the twice-punctured Riemann sphere into R^3 from the Bessel equation.

Study Hardy identities and inequalities on Cartan-Hadamard manifolds.

In this paper we study the problem of deriving further Sobolev inequalities from a given Sobolev inequality. We use several different methods, including Bessel potentials and Riesz transforms. We apply the results to the Ricci flow to extend the author's results on the $W^{1,2}$ Sobolev inequality along the Ricci flow …

We study the geometry and partial differential equations arising from the consideration of Frobenius determinants, also called-group-determinants. This leads us to address some aspects of twistor theory as well as some extensions of Bessel functions.

Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.

Develops local elliptic regularity for geometrically-natural operators with low regularity coefficients.

New findings suggest Barron space doesn't defy curse of dimensionality for certain types of smoothness.

In this paper we analytically study the problem of pricing an arithmetically averaged Asian option in the path integral formalism. By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action functional whose potential term is an exponential function. This path integral …

Given a compact Riemannian manifold (M n , g) with boundary $\partial$M , we give an estimate for the quotient $\partial$M f d$μ$ g M f d$μ$ g , where f is a smooth positive function defined on M that satisfies some inequality involving the scalar Laplacian. By the mean value lemma established in [37], we provide a dif…

This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.

New simulation method simplifies Heston model with Poisson conditioning for better accuracy and efficiency.

Following Donaldson's oppenness theorem on deforming a conical Kähler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical Kähler-Ricci Flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use t…

The paper introduces new methods for Asian option pricing using Laguerre quadrature.

This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional time-homogeneous diffusions even for the cases where the corresponding transition den…

We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDE…

This paper is motivated by questions about averages of stochastic processes which originate in mathematical finance, originally in connection with valuing the so-called Asian options. Starting with research of Yor's in 1992, these questions about exponential functionals of Brownian motion have been studied in terms of …

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper propo…

We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for probability densities of single-sided level crossing problem. The framework is applicabl…

Study phase transitions in noisy transformer dynamics on spheres.

DimeNet uses directional message passing to improve molecular predictions.

Paper solves PDEs for optimal investment strategies in volatile markets.

Study of financial models using PIDEs with and without market liquidity.

Black-box variational inference tries to approximate a complex target distribution though a gradient-based optimization of the parameters of a simpler distribution. Provable convergence guarantees require structural properties of the objective. This paper shows that for location-scale family approximations, if the targ…

New method for pricing barrier options in time-dependent λ-SABR model.

At critical coupling, the interactions of Ginzburg-Landau vortices are determined by the metric on the moduli space of static solutions. The asymptotic form of the metric for two well separated vortices is shown here to be expressible in terms of a Bessel function. A straightforward extension gives the metric for N vor…

This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant …

Solves a long-standing problem on step-two groups with exact formulas.

This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic spaces, $S_\k^3$ ($κ>0$) and $H_\k^3$ ($κ<0$), to the standard {\itshape spherical wav…

We propose two main applications of Gyöngy (1986)'s construction of inhomogeneous Markovian stochastic differential equations that mimick the one-dimensional marginals of continuous Itô processes. Firstly, we prove Dupire (1994) and Derman and Kani (1994)'s result. We then present Bessel-based stochastic volatility mod…

Model financial market with fundraiser and stock, derive option prices.

The paper examines how the angle between inputs in ReLU networks decreases with depth, impacting training.

Extends utility maximization theory for infinite horizons without strong no-arbitrage assumptions.

Paper analyzes EM algorithm's trajectory in 2MLR, revealing cycloid behavior.

Unique solutions found for diffusive martingale problems.

We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results w…

The Langevin Algorithm's stationary distribution is shown to be sub-exponential or sub-Gaussian under certain conditions.

The paper studies projections of asset prices under equivalent martingale measures.