A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study finds formulas for minimal submanifolds using Möbius transformations.
Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.
Explains affine rough models and their transform formulas.
Formulae for Bäcklund transformations of hyperbolic and elliptic sine-Gordon/sinh-Gordon equations.
Derives integral formulae on weighted manifolds.
The article provides formulas for homological blocks of Seifert fibered homology 3-spheres.
The paper derives Pizzetti formulae and inverts the Radon transform on spheres.
An index formula is proposed for contact transformations between contact manifolds equipped with CR structures or with fillings by symplectic manifolds. The formula generalizes the Atiyah-Singer formula and gives a conjectured formula for the index of Fourier integral operators, as well as Epstein's relative index for …
For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones wer…
Formula calculates higher moments of Siegel-Veech transform over Hecke triangle groups.
Researchers study horospherical transforms on hyperboloids.
Transformers learn to predict temporal logic solutions from classical solver outputs.
Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at least a Levy transformation in each direction, we get closed formulae in terms of multi-Wroński determinants. These formulae are for the tange…
The paper calculates option prices using Mellin transform for stochastic volatility models.
Darboux Wronskian formulas allow to construct Darboux transformations, but Laplace transformations, which are Darboux transformations of order one cannot be represented this way. It has been a long standing problem on what are other exceptions. In our previous work we proved that among transformations of total order on…
We give reconstruction formulas inverting the geodesic X-ray transform over functions (call it ) and solenoidal vector fields on surfaces with negative curvature and strictly convex boundary. These formulas generalize the Pestov-Uhlmann formulas in [Pestov-Uhlmann, IMRN '04] (established for simple surfaces) to ca…
Solves problem of describing transformations for upper triangular Toeplitz operators.
In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of first-generation exotic derivat…
Inverts rank m symmetric tensor fields using line integrals.
Derives an index formula for families of end-periodic Dirac operators.
The paper derives formulas for option pricing and random walk expectations.
We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equati…
Study light ray transform in pseudo-Euclidean space, derive inversion formula, and prove stability.
The article recovers tensor fields from partial data using weighted divergent ray transforms.
The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of intersections bodies in convex geometry.
Developed new Crofton formulas for pseudo-Riemannian spaces.
The article proves integral formulas for foliated sub-Riemannian manifolds.
We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE's and the Runge-Kutta al…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors are symmetric differentials of any order as well as other types obtained after ta…
Closed pricing formulas for Variance Gamma model payoffs.
A new formula reveals symmetries between mean excess and ES functions.
The paper finds transformation formulas for quaternionic complex structures.
We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms. Our transform differs from the one in Gelfand-Graev-Shapiro. Moreover, if it can …
The article derives integral formulas for foliated sub-Riemannian manifolds.
We present two range characterizations for the attenuated geodesic X-ray transform defined on pairs of functions and one-forms on simple surfaces. Such characterizations are based on first isolating the range over sums of functions and one-forms, then separating each sub-range in two ways, first by implicit conditions,…
We discuss non-conformal harmonic surfaces in with prescribed ()transforms, and we get a representation formula for non-conformal harmonic surfaces in .
The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff funct…
In this note, we give a generalization of the inversion formulas of Pestov-Uhlmann for the geodesic ray transform of functions and vector fields on simple 2-dimensional manifolds of constant curvature. The inversion formulas given here hold for 2-dimensional simple manifolds whose curvatures close to a constant.
The potential function of the optimistic limit of the colored Jones polynomial and the construction of the solution of the hyperbolicity equations were defined in the authors' previous articles. In this article, we define the Reidemeister transformations of the potential function and the solution by the changes of them…
We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.
Paper derives option pricing formula for SVJ models with jumps.
Study on contact Hamiltonian functions for singular contact structures.
New integral-geometric formulae derived from normal densities ring.
Study duality of zero mean curvature surfaces in Heisenberg group.
We give a generalization of the Penrose transform on Hermitian manifolds with metrics locally conformally equivalent to Bochner-Kähler metrics. We also give an explicit formula for the inverse transform. This paper is a generalization of "The Twistor correspondence of the Dolbeault complex over $\C^n$" (dg-ga/9501004) …
Proves loop coproduct invariance under simple homotopy equivalences.
Researchers relax the CVF's smoothness requirement to create more flexible flow models.
In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first hitting times of the dr…