We derive a new, exact and transparent expansion for option smiles, which lends itself both to analytical approximation and, perhaps more importantly, to congenial numerical treatments. We show that the skew and the curvature of the smile can be computed as exotic options, for which the Hedged Monte Carlo method is par…
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48 results for “Karhunen-Loève Expansion”
VES-Gamma adapts EI using information-theoretic principles.
problem Optimizing black-box functions using Bayesian optimization.
method Variational Entropy Search (VES) and VES-Gamma algorithm.
result VES-Gamma improves EI by incorporating information-theoretic concepts.
A new method improves estimation of COVID-19 vaccine effectiveness.
problem Estimating vaccine effectiveness under the test-negative design.
method A doubly robust estimator (TNDDR) using cross-fitting and machine learning.
result The TNDDR estimator is -consistent, asymptotically normal, and doubly robust.
We consider a mean curvature flow in a cone, that is, a hypersurface in a cone which moves toward the opening with normal velocity equaling to the mean curvature, and the contact angle between the hypersurface and the cone boundary being -periodic in its position. First, by constructing a family of self-si…
F.: Good morning Hermann, I would like to talk with you about infinitesimals. G.: Tell me Pierre. F.: I'm fed up of all these slanders about my attitude to be non rigorous, so I've started to study nonstandard analysis (NSA) and synthetic differential geometry (SDG). G.: Yes, I've read something ... F.: Ok, no problem …
Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifoldmath.GT
This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by . Firstly, we've obtained the topological classificat…
In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent the loca…
Unified framework connects EI and information-theoretic acquisition functions.
problem Distinguish between Expected Improvement and information-theoretic acquisition functions.
method Introduces Variational Entropy Search (VES) to unify EI and information-theoretic approaches.
result EI can be seen as a variational inference approximation of Max-value Entropy Search (MES).
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from readers, I've decided to make a presentable half-finished version available here.…
Lecture notes on CAT(0) cube complexes for beginners.
problem Introduction to CAT(0) cube complexes for students.
method Elementary and self-contained lectures.
result Accessible introduction to advanced topics for students.
Bitcoin Gold, Litecoin Silver:An Introduction to Cryptocurrency's Valuation and Trading Strategycs.CE
This study compares Bitcoin and Litecoin using cryptocurrency metrics and trading strategies.
problem Valuation and trading strategies for cryptocurrencies.
method Metrics like UTXO, STXO, WAL, CDD, and trading strategies based on PU ratio.
result Bitcoin's superior store-of-value proposition compared to Litecoin validated.
Study uses neural processes to predict and classify crack patterns in moving disks.
problem Predicting and classifying crack patterns in moving disks.
method Peridynamic theory, Convolutional Neural Networks (CNNs), and Neural Processes.
result Neural Processes provide accurate predictions even with missing or insufficient data.
New metrics with constant Q-curvature created by gluing.
problem Creating metrics with constant Q-curvature on spheres with punctures.
method Gluing truncated known metrics together.
result Unmarked moduli space of solutions is nontrivial for at least four punctures.
The paper analyzes the score field of diffusion models using Burgers dynamics.
problem Understanding the evolution of score fields in diffusion models.
method Analyzes the score field through Burgers-type evolution law for diffusion models.
result Identifies a universal \( anh\) interfacial term in the score field.
We consider the following singularly perturbed Neumann problem \begin{eqnarray*} \ve^2 Δu -u +u^p = 0 \, \quad u>0 \quad {\mbox {in}} \quad Ω, \quad {\partial u \over \partial ν}=0 \quad {\mbox {on}} \quad \partial Ω, \end{eqnarray*} where and is a smooth and bounded domain in . We construct a new class…
We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on proba-bilistic graphical models. These include two mechanisms for adding noise to the Bayesia…
Rescaling expansiveness proven for k*-expansive vector fields.
problem Proving rescaling expansiveness for k*-expansive vector fields.
method Introducing and exploring singular-expansive flows.
result Rescaling expansiveness established for k*-expansive vector fields.
The paper derives expansions for Green's operators and resolvents using Hadamard methods.
problem Analyzing normally hyperbolic operators and their Green's functions.
method Hadamard expansions for powers of Green's operators and resolvents.
result Derives expansions involving Hadamard coefficients for advanced/retarded Green's operators.
Nontrivial boundary Dehn twist found on K3#K3 manifold.
problem Proving nontriviality of a Dehn twist on a specific 4-manifold.
method Algebraic criterion and equivariant topological K-theory to show non-isotopy.
result Boundary Dehn twist is nontrivial in the smooth mapping class group.
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
Taylor expansions improve reinforcement learning policies.
problem Improving reinforcement learning policy optimization.
method Taylor expansion policy optimization.
result Taylor expansions enhance performance of distributed algorithms.
Analytic torsion expansions for symmetric and complex homogeneous spaces.
problem Calculating the full asymptotic expansion of analytic torsion for various spaces.
method Explicit calculation and comparison with existing results.
result Explicit full asymptotic expansions for symmetric and complex homogeneous spaces.
Proved cyclotomic expansion for double twist knots' HOMFLY-PT invariants.
problem Proving cyclotomic expansion for colored HOMFLY-PT invariants of double twist knots.
method Cyclotomic expansion formula for double twist knots.
result Confirmed cyclotomic expansion conjecture for SU(N)-invariants.
Study of hypersurfaces with specific expansion properties.
problem Existence and properties of hypersurfaces with prescribed null expansion.
method Adapted Eichmair's Perron approach for existence.
result Topology theorem for hypersurfaces with prescribed null expansion.
A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.
problem Information loss in hypergraph expansions on either vertex or hyperedge level.
method Proposes a new hypergraph formulation named line expansion (LE) that treats vertices and hyperedges symmetrically.
result The proposed line expansion method outperforms state-of-the-art baselines on five hypergraph datasets.
Study evaluates methods for expanding communities in hypergraphs using random walks.
problem Expanding communities in hypergraphs using random walks.
method Clique-expansion and tensor methods evaluated; hybrid method proposed.
result Parameter regimes identified where methods outperform each other.
Every year, thousands of people receive consumer product related injuries. Research indicates that online customer reviews can be processed to autonomously identify product safety issues. Early identification of safety issues can lead to earlier recalls, and thus fewer injuries and deaths. A dataset of product reviews …
Asymmetric expansion preserves convexity in hyperbolic geometry.
problem Maintaining convexity in hyperbolic geometry under asymmetric expansions.
method Generalizing earlier results on radial expansion to asymmetric expansion.
result Asymmetric expansion of hyperbolic convex sets remains convex.
The paper calculates asymptotic expansions for specific types of oscillatory integrals.
problem Analyzing oscillatory integrals with complex phase functions.
method Using asymptotic expansions of simpler phase functions to derive results for more complex cases.
result Explicit computation of coefficients in asymptotic expansions for certain integrals.
Dropout increases the generalization of neural networks by expanding the weight space.
problem Understanding and improving the generalization of neural networks.
method Introducing weight expansion and showing that dropout leads to it.
result Dropout increases the generalization of neural networks by expanding the weight space.
New derivation of knot invariants from universal invariant.
problem Deriving knot invariants from universal invariant.
method Using Hopf algebra and a Mathematica implementation to compute .
result Derivation of large-color expansion from universal invariant.
Functional Expansionsq-fin.MF
This work explores functional expansions to handle path dependence in various fields.
problem Path dependence and infinite-dimensional problems in non-Markovian systems.
method Generalizes Wiener series and functional Taylor expansion to handle static and dynamic functionals.
result Elegant separation of functionals from future trajectories in dynamic cases.
In the planar limit of the 't Hooft expansion, the Wilson-loop average in 3d Chern-Simons theory (i.e. the HOMFLY polynomial) depends in a very simple way on representation (the Young diagram), so that the (knot-dependent) Ooguri-Vafa partition function becomes a trivial KP tau-function. We study higher genus correctio…
On the third coefficient in the TYCZ-expansion of the epsilon function of Kaehler-Einstein manifoldsmath.DG
Paper calculates third coefficient in Kaehler-Einstein metric expansion.
problem Understanding Kaehler-Einstein metrics and their epsilon functions.
method Computes the third coefficient in the TYCZ-expansion of the epsilon function.
result Discovers the vanishing of the third coefficient's significance.
Invariants for 3D manifolds with boundaries using crossed modules.
problem Develop invariants for compact 3D manifolds with boundaries.
method Employ crossed modules to count correct colors over triangulations.
result Validated invariants for compact 3D manifolds with boundaries.
Study on heat trace expansion for thermoelastic Dirichlet-to-Neumann map.
problem Asymptotic expansion of heat trace for thermoelastic Dirichlet-to-Neumann map.
method Provided a method to obtain all coefficients of the asymptotic expansion.
result Explicitly gave the first two coefficients involving volume and total mean curvature of the boundary.
We expand volatility models for rough stochastic volatility.
problem Modeling rough stochastic volatility.
method Vol-of-vol expansion for potentially infinite dimensional models.
result Explicit representations of push-down Malliavin weights.
The paper proposes and proves asymptotic expansions for quantum invariants.
problem Quantum invariants and their expansions under varying metrics.
method Asymptotic expansion conjectures for relative Reshetikhin-Turaev, Turaev-Viro invariants and quantum 6j-symbols.
result Proved asymptotic expansions for special cases, showing geometric dependence on metrics.
SAIL improves graph node representation learning by distilling knowledge between graphs.
problem Improving graph node representation learning with GNNs in unsupervised scenarios.
method SAIL framework with intra- and inter-graph knowledge distillation.
result SAIL consistently outperforms state-of-the-art baselines on various benchmark datasets.
New method models portfolios with leptokurtic risk factors using Gram-Charlier expansions.
problem Modeling portfolios with excess kurtosis.
method GC-like expansions of the hyperbolic-secant law to account for leptokurtosis.
result Portfolio distribution with risk factors modeled as GC-like expansions of the HS law.
Develops AMITE for analyzing neural network nonlinearities.
problem Addressing difficulties in verification, explainability, and security in neural network analysis.
method Analytically modified integral transform expansion (AMITE) for neural network nonlinearities.
result First to provide six mutually exclusive desired expansion properties.
Paper presents new expansions for option pricing with cash dividends.
problem No exact formula for European options with cash dividends.
method Uses Etore and Gobet's technique for piecewise lognormal process with jumps.
result Provides more robust first, second, and third-order expansions.
We survey recent results about the asymptotic expansion of Toeplitz operators and their kernels, as well as Berezin-Toeplitz quantization. We deal in particular with calculation of the first coefficients of these expansions.
The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validat…
The paper uses polyhedral expansions to capture the shape of compact metric spaces.
problem Capturing the shape of compact metric spaces using finite approximations.
method Inverse sequences of polyhedra based on finite approximations of a compact metric space.
result Proves the General Principle and computes inverse persistent homology groups.
We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kern…
We quantify predictive uncertainty using the posterior predictive variance.
problem Quantifying uncertainty in predictive models.
method Using the law of total variance, we generate expansions for the posterior predictive variance.
result Identify the main contributors to prediction intervals and quantify term-wise uncertainty.
The study improves volatility model pricing accuracy with new statistical expansions.
problem Improving option pricing accuracy in volatility models.
method Developed Edgeworth expansions for various volatility models.
result Enhanced statistical expansions for volatility models.