Ghost points affect stability in finite difference schemes for diffusion equations.
problem Impact of ghost points on stability of finite difference schemes.
method Exploration of explicit Euler finite difference scheme with ghost points on diffusion equation.
result Stability of the scheme is affected by ghost points.
Study on numerical analysis for corporate bonds using a unified 2 factor model.
problem Develop a numerical method to solve a unified 2 factor model for corporate bonds with fixed discrete coupons.
method Used explicit finite difference scheme to analyze stability and compute bond prices.
result Found conditions for the explicit finite difference scheme to be stable and computed bond prices, credit spread, and duration.
Study binomial tree and explicit difference schemes for American options with time-dependent volatility.
problem Modeling American options with time-dependent volatility using binomial tree and explicit difference schemes.
method Developed a time interval partition method for binomial tree dynamics and proved convergence to viscosity solutions.
result Proved monotonic and decreasing/increasing properties of American option prices and exercise boundaries on time variable.
Develops a new option pricing model under G-expectation framework.
problem Modeling uncertainty in financial markets and robust valuation under model uncertainty.
method G-expectation framework, logarithmic transformation, finite difference schemes.
result Unified risk-neutral valuation approach yielding G-Black-Scholes equation.
Estimates error for American option pricing using finite differences.
problem Valuation of American options with numerical methods.
method Explicit finite difference scheme with Richardson extrapolation error estimator.
result Determines suitable grid for error tolerance in option pricing.
Develops a finite difference scheme for Hambit fields in Hilbert space.
problem Representation and approximation of ambit fields in Hilbert space.
method Lifts ambit fields to Hilbert space-valued Volterra processes, interprets them as solutions of stochastic PDEs, and develops a finite difference scheme.
result Finite difference scheme for Hambit fields converges under Lipschitz conditions.
We identify the difference between the CM polarisation and the Chow polarisation on the ``Hilbert scheme''. As a consequence, we give a numerical criterion for the CM stability as in Mumfords' G.I.T.. Also, we write down an explicit formula for the generalised futaki invariant interms of weights and multiplicities of t…
A new explicit scheme calculates XVA adjustments using neural networks and conditional expectations.
problem Calculating cross valuation adjustments (XVA) in realistic financial scenarios.
method Simulation/regression scheme for BSDEs, using neural networks and quantile regressions.
result The scheme outperforms Picard iterations in high-dimensional and hybrid market risks.
New boundary treatment improves accuracy for complex PDEs.
problem Order reduction in high-order IMEX schemes for multidimensional PDEs.
method Novel boundary treatment algorithms for Cartesian meshes, treating implicit-explicit stages similarly to interior points.
result Recovery of designed order of convergence by numerical verification.
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.
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by solving various problems in many fields, which can be hardly handled by alternati…
A new method for pricing options with stochastic volatility and jumps.
problem Pricing options under stochastic volatility and jumps.
method Fourth-order compact finite-difference scheme with implicit-explicit Crank-Nicolson framework.
result The method achieves near-fourth-order spatial accuracy and up to two orders of magnitude lower runtime than quadratic finite elements.
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.
A new subdivision scheme for Heisenberg group values with central smoothness loss.
problem Regularity of limit curves in Heisenberg group-valued subdivision schemes.
method Interpolatory subdivision scheme with central correction based on group law.
result Central part of limit curve converges to a continuous limit with logarithmic modulus of continuity.
We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity and integrability conditions, we obtain the opt…
INFERS PDEs from data samples using learned context.
problem Inferring explicit PDEs from unseen dynamics.
method Contextual Finite Differences (CFD) method integrating PDE form and differential scheme.
result Yields a PDE fitting the data sample for signal prediction and explanation.
Constructs k-regular maps using algebraic geometry.
problem Determine the minimal value of N for k-regular maps from R^m to R^N.
method Algebraic geometry methods to construct k-regular maps and relate upper bounds to the dimension of Gorenstein schemes.
result Explicit examples and upper bounds for k-regular maps for k<6 and arbitrary m and k.
Novel IMEX scheme solves financial PDEs with mixed derivatives.
problem Numerical approximations for financial PDEs with mixed derivatives.
method Second order finite volume IMEX Runge-Kutta scheme.
result Achieves true second order convergence with non-regular initial conditions.
Continuous-time PCD for MLE with explicit error bounds.
problem Maximum likelihood estimation of unnormalised densities.
method Continuous-time formulation as coupled SDEs, deriving UiT bounds.
result Explicit error bounds between PCD iterates and MLE solution.
The paper presents two schemes for sampling matrices from specific distributions on a manifold.
problem Sampling matrices from Gibbs distributions on the manifold of positive semi-definite matrices with fixed rank.
method Two explicit schemes based on Euler-Maruyama discretization of the Riemannian Langevin equation with Brownian motion on the manifold.
result Numerical validation of the schemes using specific energy functions and metrics.
New method preserves positivity in financial model simulations.
problem Preserving positivity in financial model simulations.
method Combining semi discrete technique with split step method.
result Explicit and positivity preserving numerical scheme for Ait-Sahalia model.
New framework monitors neural network training and reveals regularisation mechanisms.
problem Overfitting in neural networks and the need for explicit regularizers.
method Model Gradient Similarity (MGS) framework to measure and monitor regularisation.
result Explicit regularizers increase Model Gradient Similarity (MGS).
New method solves complex financial option pricing with varying time steps.
problem Pricing American options with varying time steps and regime switching.
method Explicit Runge-Kutta-Fehlberg scheme with fourth-order compact finite difference in space and high order analytical approximation.
result The method provides better performance in terms of computational speed and accuracy.
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 compact finite difference scheme outperforms standard methods in Bates model hedging.
problem Improving hedging performance in Bates model option pricing.
method High-order compact finite differences compared to standard finite differences.
result The new scheme outperforms standard methods in all experiments.
Note on instabilities in super-time-stepping methods for Heston model.
problem Instabilities in super-time-stepping methods applied to Heston model.
method Exploration of explicit super-time-stepping schemes (RK-Chebyshev, RK-Legendre) for Heston model.
result Relevance of stability remarks beyond super-time-stepping schemes.
The coupled system, where one is a degenerate parabolic equation and the other has not a diffusion term arises in the modeling of European options with liquidity shocks. Two implicit-explicit (IMEX) schemes that preserve the positivity of the differential problem solution are constructed and analyzed. Numerical experim…
The paper develops and tests operator splitting schemes for American options in a complex model.
problem Efficient numerical solution of American options under a two-asset Merton jump-diffusion model.
method Adaptation of IMEX and ADI operator splitting schemes to solve the two-dimensional PIDCP.
result Investigates and compares the convergence and performance of eight operator splitting methods.
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.
Robust PDE method for path-dependent Asian-style options using MPDATA.
problem Valuation of path-dependent Asian-style options.
method Non-oscillatory forward-in-time second-order MPDATA finite-difference scheme for solving 2D PDEs.
result MPDATA scheme improves solution over first-order upwind step, highlighting its importance.
Proposes a new model for better speech segmentation.
problem Improving speech segmentation accuracy.
method Integrates recurrent explicit duration variables into rSLDS and uses Pólya-gamma augmentation for inference.
result Demonstrates improved segmentation on various datasets.
Families of explicit solutions are found to a nonlinear Black-Scholes equation which incorporates the feedback-effect of a large trader in case of market illiquidity. The typical solution of these families will have a payoff which approximates a strangle. These solutions were used to test numerical schemes for solving …
Stan models are compiled to generative languages and extended with new features.
problem Lack of direct support for variational inference and deep models in Stan.
method Comprehensive compilation scheme to convert Stan models to generative languages, and extension of Stan with new features.
result NumPyro backend yields a 2.3x speedup compared to Stan in geometric mean over 26 benchmarks.
Typically options with a path dependent payoff, such as Target Accumulation Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper describes a finite difference scheme for pricing a TARN option. Key steps in the proposed scheme involve tracking of multiple one-dimensional finite difference solutions,…
Novel approach ensures stability of compact schemes for variable PDEs.
problem Ensuring stability of compact schemes for variable coefficient PDEs.
method Difference equation approach to derive stability conditions.
result Derives sufficient condition for unconditional stability.
New high-order scheme for option pricing in stochastic volatility jump models.
problem Option pricing in stochastic volatility jump models.
method High-order compact finite difference scheme.
result The new scheme outperforms standard methods in efficiency and accuracy.
New discretization scheme for Wasserstein gradient flows using Schrödinger bridges.
problem Computing Wasserstein gradient flows efficiently and without score functions.
method Iterated Schrödinger bridge approximation with particle-based Sinkhorn algorithm.
result The scheme converges to Wasserstein gradient flows for certain flows, including heat flow.
Paper optimizes distributed learning by reducing gradient computation time.
problem Efficiently compute gradients in distributed learning tasks.
method Recursive polynomial constructions for coding across data subsets and vector components.
result Optimal tradeoff between computation load, straggler tolerance, and communication cost achieved.
Develops explicit formulas for minimal immersions in 5D space.
problem Minimal surface models in 5D space.
method Holomorphic null curves in C^5.
result Concrete formulas for conformal minimal immersions in R^5.
A novel federated learning framework resolves structural misalignment in model fusion.
problem Structural misalignment in model fusion due to chaotic information distribution.
method Feature-oriented regulation method (Ψ-Net) to ensure feature information allocation and dedicated collaboration schemes. result Effective enhancement of federated learning applicability to heterogeneous settings with improved convergence speed, accuracy, and efficiency.
New metric estimates user satisfaction for dialogue quality evaluation.
problem Sparse and intrusive explicit user feedback for dialogue quality evaluation.
method Created a new Response Quality annotation scheme and developed a turn-level User Satisfaction metric using five domain-independent feature sets and six machine learning models.
result Gradient boosting regression achieved best correlation of ~0.79 between predicted and annotated user satisfaction labels.
The Runge-Kutta-Legendre scheme improves pricing American options and other derivatives.
problem Pricing American options and other derivatives with improved accuracy and stability.
method Runge-Kutta-Legendre finite difference scheme applied to Black-Scholes and Heston models.
result Improved convergence and stability compared to existing schemes.
This paper investigates the classical and quantum elementary systems with Newton-Hoooke symmetry. A complete classification is given by explicit computation. In addition, we present an application example of quantization using the Moyal scheme.
Link slope stability to Donaldson's functional via Quot-scheme limits.
problem Establishing a connection between slope stability and Donaldson's functional for vector bundles.
method Defining Quot-scheme limits of Fubini-Study metrics and proving Donaldson's functional's coercivity.
result Donaldson's functional is coercive on Fubini-Study metrics for slope stable bundles.
Compact scheme solves fractional Black-Scholes on non-uniform grids.
problem Solving time-fractional Black-Scholes equation on non-uniform grids.
method Three-point compact finite difference scheme on graded meshes.
result Fourth-order accuracy in space for special meshes.
We give a new proof of the Jantzen sum formula for integral representations of Chevalley schemes over Spec Z. This is done by applying the fixed point formula of Lefschetz type in Arakelov geometry to generalized flag varieties. Our proof involves the computation of the equivariant Ray-Singer torsion for all equivarian…
New symplectic scheme speeds up RMHMC.
problem Reducing computational burden in RMHMC.
method Explicit symplectic integration for non-separable Hamiltonians.
result Significant reduction in higher-order derivative calculations.
Proposes a new deep neural network training scheme combining different loss functions.
problem Improving generalization ability of deep neural networks.
method Integrates multiple loss functions in a nonlinear manner.
result The new objective function enhances optimization and generalization.