Paper proves strong convergence of Ninomiya-Victoir scheme and proposes an improved multilevel estimator.
problem Strong convergence analysis of Ninomiya-Victoir scheme and optimization of multilevel Monte Carlo estimators.
method Proves strong convergence of order 1/2 for Ninomiya-Victoir scheme and proposes a modified scheme with strong coupling to Giles-Szpruch scheme.
result Improves efficiency of multilevel Monte Carlo estimators by reducing the number of discretization levels.
New high-order scheme reduces BSDE truncation errors.
problem Numerical solution of backward stochastic differential equations (BSDEs).
method Proposes a new θ θ θ -scheme with careful θ θ θ selection for every subinterval. result Error estimates and verification of scheme order.
Paper proposes a new numerical scheme for solving BSDEs.
problem Solving backward stochastic differential equations (BSDEs).
method Uses Lagrange interpolation to approximate derivatives and changes sample point distributions for different stability and convergence.
result Guarantees convergence of the scheme under certain conditions on sample point distributions.
Improved scheme for option pricing in stochastic volatility models with jumps.
problem Efficiently pricing options in models with stochastic volatility and jumps.
method Developed a high-order compact finite difference scheme for SVCJ models.
result Achieves fourth order convergence compared to standard schemes.
New probabilistic scheme combines deep learning with Runge-Kutta methods for solving PDEs.
problem Solving high-dimensional semi-linear parabolic PDEs efficiently.
method Probabilistic scheme using deep learning and Runge-Kutta methods.
result Crank-Nicolson schemes are efficient in terms of precision, computational cost, and numerical implementation.
It was proved in 1998 by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same…
Reduces multiclass and regression compression schemes to binary ones.
problem Developing efficient learning algorithms for multiclass and regression problems.
method Reduces sample compression schemes for binary classes to multiclass and regression settings.
result Establishes new compression schemes for multiclass and regression problems.
Study SL(2,C) character schemes for finitely generated groups.
problem Characterize SL(2,C) representations of finitely generated groups.
method Define coordinate rings and equations for SL(2,C) character schemes.
result Explicit equations for character schemes of finitely presented groups.
A new method for computing image curvature efficiently and accurately.
problem Low performance, low accuracy, and requirement of second order differentiability in conventional computation schemes.
method Proposes a novel discrete computation scheme for weighted Gaussian curvature.
result More accurate, computationally more efficient, and does not require second order differentiability.
Symplectic discretization accelerates optimization of smooth convex functions.
problem Optimizing smooth convex functions efficiently.
method Discretizing Nesterov's and Polyak's methods using Euler and symplectic schemes.
result Symplectic discretization achieves accelerated optimization for smooth convex functions.
Study evaluates UK CDC schemes, finding intergenerational cross-subsidies in flat-accrual schemes and dynamic-accrual schemes can reduce but not eliminate them.
problem Intergenerational cross-subsidies in UK CDC schemes, particularly in flat-accrual schemes.
method Comparison of flat-accrual and dynamic-accrual CDC schemes, analysis of performance and level of cross-subsidies.
result Dynamic-accrual schemes can reduce but not eliminate intergenerational cross-subsidies, while flat-accrual schemes often have significant cross-subsidies.
New high-order compact scheme improves basket option pricing accuracy.
problem Improving accuracy in pricing European Put options on a basket of assets.
method Developed a second-order accurate in time and fourth-order accurate in space high-order compact scheme.
result Standard second-order schemes are significantly outperformed by the new scheme.
AES scheme improves Bermudan and American option pricing for Heston models.
problem Pricing Bermudan and American options under Heston models efficiently.
method AES scheme using non-central chi-square distribution for variance process.
result AES achieves higher accuracy and computational efficiency for Bermudan options.
Generalizes soft noncommutative schemes to flag varieties.
problem Applying soft noncommutative schemes to flag varieties.
method Generalization via toric geometry and distinguished affine charts.
result Soft noncommutative schemes can be applied to flag varieties.
Defines hypercomplex analytic spaces and schemes.
problem No specific problem stated; focuses on definitions.
method Definitions and quotient construction.
result Canonical association of hypercomplex spaces to quotients.
New schemes for SDEs on manifolds keep solutions close to the manifold.
problem Solving SDEs constrained to manifolds in high accuracy.
method Geometrically invariant numerical schemes that remain close to the manifold.
result The schemes converge under standard assumptions and outperform existing methods.
Characterizes Hilbert schemes and their geometric properties.
problem Understanding transverse Hilbert schemes and their geometric properties.
method Characterization through bi-Poisson structures and hyperkähler geometry.
result Characterization of transverse Hilbert schemes and description of their hyperkähler geometry.
Vector fields on schemes have flows if rings are finitely generated.
problem Understanding vector fields and flows on schemes.
method Analyzing vector fields on affine C ∞ C^\infty C ∞ -schemes with finitely generated rings. result Vector fields on affine C ∞ C^\infty C ∞ -schemes with finitely generated rings have flows and are groupoid internal maps. Extends JKO scheme for iterative algorithms with unknown parameters.
problem Computational and statistical analysis of iterative algorithms with unknown parameters.
method Develops statistical methods to estimate unknown parameters and adapts JKO scheme.
result Establishes asymptotic theory for the statistical JKO scheme.
A new scheme for FBSDEs simplifies computation without Monte Carlo.
problem Numerical solution for decoupled FBSDEs with reduced complexity.
method Recursive marginal quantization for fully quantization-based scheme.
result Effective numerical procedure for financial applications.
A hybrid scheme improves accuracy in simulating Brownian semistationary processes.
problem Simulating Brownian semistationary processes with high accuracy.
method Discretizing the stochastic integral representation using a hybrid scheme of power and step functions.
result The hybrid scheme leads to a substantial improvement in accuracy compared to the forward Riemann-sum scheme.
A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically from finance, especially for path-dependent option pricing. The scheme is simple…
Study on statistical estimation over Gaussian MAC, comparing analog and digital schemes.
problem Distributed minimax statistical estimation over a Gaussian MAC.
method Developed analog joint estimation-communication schemes and derived information-theoretic lower bounds.
result Achieved risk within a logarithmic factor of information-theoretic lower bounds.
Efficient simulation scheme for rough Heston model reduces computational cost.
problem Accurate and efficient simulation of the rough Heston model for option pricing.
method Weak simulation scheme based on Markovian approximations of the rough Heston process.
result The new scheme exhibits second order weak convergence with linear computational cost.
Study finds risk management significantly improves pension scheme efficiency in Kenya.
problem Improving efficiency of pension schemes in Kenya.
method Panel data analysis of 128 pension schemes from 2015-2021.
result Risk management significantly mediates the relationship between corporate governance and pension scheme efficiency.
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier options. For getting the static hedging formula, the underlying process needs to have…
The paper analyzes convergence of Riemannian SA schemes for stochastic optimization.
problem Stochastic optimization problems on Riemannian manifolds.
method Analyzes convergence of Riemannian stochastic approximation schemes using exponential map or retraction functions.
result Shows Riemannian SA schemes find an O ( b ∞ + log n / n ) {\mathcal{O}}(b_\infty + \log n / \sqrt{n}) O ( b ∞ + log n / n ) -stationary point within O ( n ) {\mathcal{O}}(n) O ( n ) iterations. New CDC scheme avoids intergenerational subsidies, offering better outcomes.
problem Intergenerational cross-subsidies in UK CDC schemes.
method Collective-Drawdown CDC approach using explicit insurance contracts.
result Better pension outcomes with no intergenerational cross-subsidies.
Develops theory of differential graded schemes for derived stacks.
problem Creating a theory for derived stacks using dg schemes.
method Formulates dg schemes as homotopy sites, equates to stacks on dg algebras.
result Infinity category of stacks represented by dg schemes is derived schemes.
Strictification of isotropic distributions on derived schemes with shifted symplectic forms.
problem Understanding isotropic distributions on derived schemes with specific symplectic structures.
method Proving strictification result for isotropic distributions on derived schemes equipped with negatively shifted homotopically closed 2-forms.
result Derived schemes with − 2 -2 − 2 -shifted symplectic structures globally admit Lagrangian distributions. We introduce (binary) Darboux transformation for general differential equation of the second order in two independent variables. We present a discrete version of the transformation for a 6-point difference scheme. The scheme is appropriate to solving a hyperbolic type initial-boundary value problem. We discuss several …
A risk of small defined-benefit pension schemes is that there are too few members to eliminate idiosyncratic mortality risk, that is there are too few members to effectively pool mortality risk. This means that when there are few members in the scheme, there is an increased risk of the liability value deviating signifi…
We develop high-order approximations for the Heston model.
problem Modeling the Heston model with high accuracy and efficiency.
method Combining approximation schemes on different random grids to achieve any order of convergence.
result Achieve any order of convergence for the Heston model.
High-order compact schemes improve option pricing accuracy for stochastic volatility models.
problem Improving option pricing accuracy for stochastic volatility models with non-uniform grids.
method Fourth-order accurate compact schemes applied to option pricing PDEs for stochastic volatility models on non-uniform grids.
result Fourth-order accuracy achieved for non-zero correlation, outperforming standard schemes.
We study the performance of the adaptive construction scheme for a Bayesian inference on the Quadratic GARCH model which introduces the asymmetry in time series dynamics. In the adaptive construction scheme a proposal density in the Metropolis-Hastings algorithm is constructed adaptively by changing the parameters of t…
Improved accuracy in quantization methods for financial derivatives.
problem Efficient numerical methods for evaluating functionals of stochastic differential equations.
method Recursive Marginal Quantization of higher-order schemes (Euler, Milstein, simplified weak order 2.0).
result Higher-order schemes provide improved weak order convergence and accurate marginal distributions.
New systems derived from Hilbert schemes on surfaces.
problem Characterizing completely integrable systems on surfaces.
method Using transverse Hilbert schemes to associate systems to surfaces.
result Characterized completely integrable systems arising from Hilbert schemes.
New schemes improve vertex nomination in stochastic block models.
problem Ordering vertices with unknown labels in a network.
method Canonical sampling and extended spectral nomination schemes.
result Improved precision and scalability of vertex nomination schemes.
IMEX schemes preserve positivity for European options with liquidity shocks.
problem Modeling European options with liquidity shocks.
method Two implicit-explicit (IMEX) schemes that preserve positivity are constructed and analyzed.
result The schemes confirm high accuracy and efficiency with Richardson extrapolation.
Paper proposes an efficient PCA method for memory-limited streaming data.
problem Memory-limited online PCA methods struggle with convergence and eigenvector extraction.
method A single-pass algorithm converging to the first k eigenvectors without predefined parameters.
result Empirical results show the scheme converges to first k eigenvectors in a single pass.
Develops SDYM equations on self-dual backgrounds using integration techniques.
problem Integrating SDYM equations on self-dual backgrounds.
method Combining SDYM integration schemes with multidimensional dispersionless integrable equations.
result Defines generating differential form and develops dressing scheme.
Two new coding schemes improve the efficient communication of noisy data.
problem Efficient communication of noisy data in machine learning.
method Ordered Random Coding (ORC) and Hybrid Coding Scheme.
result Improved coding schemes over existing approaches.
This paper studies parallelization schemes for stochastic Vector Quantization algorithms in order to obtain time speed-ups using distributed resources. We show that the most intuitive parallelization scheme does not lead to better performances than the sequential algorithm. Another distributed scheme is therefore intro…
Paper develops a finite dimensional approximation scheme for Riemannian manifolds.
problem Integration on Riemannian manifolds.
method New finite dimensional approximation scheme motivated by categorical colimit.
result Establishes a generalization for L 1 L^{1} L 1 -functionals on Riemannian manifolds. Paper proves convergence of measure transfer schemes using slicing and matching.
problem Iterative schemes for measure transfer and approximation problems.
method Slicing-and-matching procedure, stochastic gradient descent on Wasserstein space.
result Almost sure convergence proof for stochastic slicing-and-matching schemes.
Geometric models for algebraic suspensions using affine deformation spaces.
problem Analyzing which motivic homotopy types have smooth scheme representatives.
method Affine deformation spaces of embeddings provide models for P 1 {\mathbb P}^1 P 1 -suspensions of schemes. result Yields many examples of A 1 {\mathbb A}^1 A 1 -connected and strictly quasi-affine schemes. Study optimal investment strategy for pension schemes to hedge longevity risk.
problem Hedging longevity risk in defined contribution pension schemes.
method Transformed optimal investment problem into an unconstrained problem using dynamic programming and numerical studies.
result Longevity risk significantly impacts investment strategies, supporting the use of mortality-linked securities.
New bounds found for agnostic learning with sample compression schemes.
problem Finding optimal rates of convergence for agnostic learning.
method Established tight characterization of worst-case rates for agnostic learning with sample compression schemes.
result Optimal rates of convergence for size- k k k agnostic sample compression schemes are k log ( n / k ) n \sqrt{\frac{k \log(n/k)}{n}} n k l o g ( n / k ) .