We derive formulas for F measures' standard error and confidence intervals.
problem Estimating F measures' accuracy with confidence.
method Analytic formulas based on asymptotic normality.
result Valid formulas for sample size planning.
On-device research index
arXiv research
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.
169,181 papers · 148 categories
Trend · papers per month
48 results for “Standard Formula”
Paper proposes a capital allocation formula for insurance companies compliant with Solvency II.
problem No specific capital allocation formula is provided for insurance companies using the Solvency II Standard Formula.
method Develops a closed formula for capital allocation that is coherent with Solvency II requirements.
result Demonstrates that the proposed allocation formula is consistent with the Euler's allocation principle.
Derives pricing formulae for power binary and normal distribution standard options.
problem Developing pricing models for binary and standard options.
method Incorporates Buchen's formulae into power binary options and derives a formula for normal distribution standard options.
result Derives pricing formulae for power binary and normal distribution standard options.
The paper proves monotonicity formulas for solutions in Carnot groups, resembling well-known formulas for standard Laplacian and heat equations.
problem Proving monotonicity formulas for solutions in Carnot groups.
method Using right-invariant carré du champ and comparing to known formulas for standard Laplacian and heat equation.
result Theorems 1.1 and 1.2 display a resemblance to known monotonicity formulas for standard Laplacian and heat equation.
New principle for supersymmetric localization on Lie groups.
problem Computing supertrace of non-supersymmetric observables.
method Invariant supersymmetric deformations and fermionic zero modes.
result Path integral localizes to periodic orbits.
New formulas derived for Jones polynomial of rational links.
problem Calculating the Jones polynomial of rational links.
method Colored Brylawski's tensor product formula for Tutte polynomials, finite automaton for crossing signs.
result Generalization of existing formulas for rational links.
-torsion of fibrationsmath.GT
The paper examines -torsion in fibration cases relaxing standard conditions.
problem Analyzing -torsion in fibrations under relaxed conditions.
method Proves sum and product formulas for -torsion in an extended abelian category.
result Obtains a formula for -torsion of a simple fibration with zero Euler characteristic.
We investigate the geometry and topology of a standard moduli space of stable bundles on a Riemann surface, and use a generalization of the Verlinde formula to derive results on intersection pairings.
Invariant operators on manifolds with almost Hermitian symmetric structures, III. Standard operatorsmath.DG
This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost quaternionic geometries. Exploiting some finite dimensional representation theory of sim…
Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions. Svensson [7] has shown that this formula simplifies to a Bochner type formula when we are dealing with Kähler manifolds and holomorphic (integrable) distributions. Here, …
An ensemble approach learns vector-weighted formulae for RLR.
problem Learning Relational Logistic Regression (RLR) with vector-weighted features.
method Functional-gradient boosting methods for probabilistic logic models.
result Our approach outperforms other methods for learning RLR.
Formula derived for Dirac operators on Lie groupoids.
problem Equivariant Dirac operators on Lie groupoids.
method Getzler rescaling method to derive a fixed-point formula.
result Reduces to standard fixed-point formula for closed manifolds.
We construct a Seifert surface for a given null-homologous transverse link in a contact manifold that is compatible with a planar open book decomposition, then obtain a formula of the self-linking number. It extends Bennequin's self-linking number formula for braids in the standard contact 3-sphere.
We find a self-linking number formula for a given null-homologous transverse link in a contact manifold that is compatible with either an annulus or a pair of pants open book decomposition. It extends Bennequin's self-linking formula for a braid in the standard contact -sphere.
New IBP formulae for rough stochastic Volterra processes.
problem Deriving IBP formulae for path-dependent stochastic Volterra processes.
method Developed a new fractional IBP formula that interpolates between standard and Bismut-Elworthy-Li formulae.
result For rough noise, the expectation is differentiable along constant directions under certain Hölder continuity conditions.
We develop two types of integral formulas for the perimeter of a convex body K in planar geometries. We derive Cauchy-type formulas for perimeter in planar Hilbert geometries. Specializing to H^2 we get a formula that appears to be new. We show that it implies the standard Cauchy-Santalo formula involving a central ang…
Study on hyperbolic manifolds with special boundaries.
problem Characterizing geometric properties of hyperbolic manifolds with specific boundaries.
method Analyzing asymptotically hyperbolic manifolds with a horospherical boundary.
result Derived geometric formulas for the model case of horoballs and their complements.
We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor calculus is the natural induced bundle calculus associated to the …
We give a formula of 3-dimensional invariant for a cyclic contact branched covering of the standard contact S^{3}.
We compute first variation formulas for the complex components of the Bakry-Emery-Ricci endomorphism along Kähler structures. Our formulas show that the principal parts of the variations are quite standard complex differential operators with particular symmetry properties on the complex decomposition of the variation o…
A new formula detects differences between counterexamples and standard embeddings of circles.
problem Detecting differences between counterexamples and standard embeddings of circles.
method Introducing a Gauss diagram formula for two-component links.
result A desired function is found for the two-component case.
A derivation of the Black-Scholes option pricing model using a central limit theorem argumentq-fin.GN
Derives Black-Scholes model using central limit theorem.
problem Deriving the Black-Scholes formula for European options.
method Central limit theorem argument for undergraduate understanding.
result Elementary derivation accessible to undergraduates.
Formula calculates index for CR operators on surfaces with boundary punctures.
problem Computing the index for Cauchy-Riemann operators on surfaces with boundary punctures.
method Large antilinear deformations method, generalized to punctured surfaces.
result Involves a non-standard weighted count of boundary zeros in the Euler characteristic term.
We consider a standard optimal investment problem in a complete financial market driven by a Wiener process and derive an explicit formula for the optimal portfolio process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is t…
Two new rational formulae for normal implied volatility are presented.
problem Calculating normal implied volatility using iterative methods.
method Two explicit rational formulae that avoid iteration and logarithms.
result Accurate and fast formulae for normal implied volatility.
Proves a formula linking LMO invariants of spliced 3-spheres.
problem Universal finite-type invariants of rational homology 3-spheres.
method Uses techniques from rational surgery and satellite formulas.
result Reveals non-additivity of the second term in the Ohtsuki series.
Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress testsq-fin.CP
Paper uses MLMC for SCR calculation and stress tests, showing computational efficiency.
problem Computing SCR and stress tests for insurance companies.
method Multilevel Monte-Carlo (MLMC) estimator for maximum of conditional expectations.
result MLMC estimator is computationally more efficient and avoids regression issues.
Explicit formulas found for ancient solutions of heat equation.
problem Finding explicit formulas for ancient solutions of the heat equation.
method Explicit representation formulas for positive ancient solutions in Euclidean and Riemannian cases.
result Ancient solutions are the Laplace transform of positive solutions of a family of elliptic operators.
The purpose of this article is to give an explicit formula for all curves of constant torsion in the unit two-sphere . These curves and their basic properties have been known since the 1890's, and some of these properties are discussed in the Appendix. Some example curves, computed with a standard ODE packa…
We give a Riccati type formula adapted for two metrics having the same geodesics rays starting from a point or orthogonal to an hypersurface, one of these metrics being a warped product if the dimension is greater than or equal to 3. This formula has non-trivial geometric consequences such as a positive mass type t…
Topological proof of Weil-Petersson symplectic form using Fenchel-Nielsen coordinates.
problem Proving Wolpert's formula for the Weil-Petersson symplectic form.
method Introducing a cell decomposition and groupoid cocycle on a surface to represent points in Teichmüller space.
result Topological proof of Wolpert's formula for the Weil-Petersson symplectic form.
We introduce the notion of Ricci-corrected differentiation in parabolic geometry, which is a modification of covariant differentiation with better transformation properties. This enables us to simplify the explicit formulae for standard invariant operators given in work of Cap, Slovak and Soucek, and at the same time e…
Paper derives option pricing formula for SVJ models with jumps.
problem Option pricing for models with finite activity jumps.
method Generic decomposition and explicit approximation formulas for SVJ models.
result Improved computation efficiency and insight into volatility smiles.
Improved option pricing formula using relativistic mechanics.
problem Improving Black-Scholes formula for better option pricing accuracy.
method Developed a relativistic version of the Black-Scholes formula and derived a closed-form solution.
result New formula offers significant improvements over existing solutions and better fits empirical data.
The paper calculates the number of closed cycles in a specific complex group.
problem Counting closed cycles in a complex group structure.
method Defined edge zeta function and used rational function formula.
result Obtained exact formula for the number of closed cycles.
In a 2006 article (\cite{A1}), Allouba gave his quadratic covariation differentiation theory for Itô's integral calculus. He defined the derivative of a semimartingale with respect to a Brownian motion as the time derivative of their quadratic covariation and a generalization thereof. He then obtained a systematic diff…
A new cohomological formula for helicity in reveals the effect of a diffeomorphism on helicitymath.GT
The helicity of a vector field is a measure of the average linking of pairs of integral curves of the field. Computed by a six-dimensional integral, it is widely useful in the physics of fluids. For a divergence-free field tangent to the boundary of a domain in 3-space, helicity is known to be invariant under volume-pr…
The paper proves formulas for determinant determinants of Laplacians on Riemann surfaces with conical singularities.
problem Determinants of Laplacians on Riemann surfaces with conical singularities.
method Polyakov-Alvarez type comparison formulas for determinants of Friedrichs extensions of Laplacians.
result Determine how determinants depend on conical singularities and provide explicit formulas.
The paper calculates factor loading and unique variance covariances for various factor analysis methods.
problem Estimating the asymptotic covariances of unrotated factor loading and unique variance estimates.
method Explicit formulas derived from sample covariances or correlations, using least square, principal, iterative principal component, alpha, or image factor analysis.
result The formulas produce reasonable standard errors for rotated loading estimates in multivariate normal populations.
We derive a formula for liquidity providers' payoff on DEXs, linking it to volatility.
problem Liquidity providers on DEXs are undercompensated for their service.
method We derive a payoff formula for liquidity providers on DEXs, assuming geometric Brownian price movements and zero arbitrage.
result The payoff from liquidity fees is a near-linear function of volatility.
A new, simple method to compute a knot invariant.
problem Computing a powerful knot invariant efficiently.
method Using a quadratic expression in the entries of the inverse of a standard matrix.
result The method leads to a powerful knot invariant with concise formulas.
We consider a consider the case of a compact manifold M, together with the following data: the action of a compact Lie group H and a smooth H-invariant distribution E, such that the H-orbits are transverse to E. These data determine a natural equivariant differential form with generalized coefficients J(E,X) whose prop…
New hyperbolic tangent formula for Black and Scholes call function.
problem Approximating the Black and Scholes call function with high accuracy.
method Developed a standardized call function and used hyperbolic tangents for approximation.
result Numerical estimation of approximating error and comparison with existing methods.
A new option pricing model uses a time-varying Hurst exponent for more accurate financial predictions.
problem Inaccurate modeling of financial time series due to constant memory parameter limitations.
method Modeling price fluctuations with multifractional Brownian motion and deriving option pricing formula.
result Empirical performance shows the multifractional model fits market quotes better than standard models.
Generalizes double transgression formulas on complex manifolds.
problem Currential double transgression formulas on complex manifolds.
method General framework using Bott-Chern Duality.
result Complements existing transgression formulas and provides new applications.
In this paper we show how to combinatorically compute the rotation class of a large family of embedded Legendrian tori in with the standard contact form. In particular, we give a formula to compute the Maslov index for any loop on the torus and compute the Maslov number of the Legendrian torus. These for…
Let M be a Kaehler manifold with a free, holomorphic and Hamiltonian action of the standard n-torus T. We give a simple, explicit and canonical formula for the Kaehler potential on the Kaehler reduction of M. As a consequence we can derive improvements of several classical results known for more general Hamiltonian red…
Parallel (co-)tractors and the geometry of first BGG solutions on almost Grassmannian structuresmath.DG
Study parallel tractors and cotractors on almost Grassmannian structures.
problem Characterize parallel tractors and cotractors on almost Grassmannian structures.
method Provide explicit formulae for splitting operators, first BGG operators, and prolongation connections. Characterize solutions of the BGG operators geometrically.
result Describe the geometry of the zero locus of solutions of the first BGG operators.