Motivated by weak convergence results in the paper of Takahashi and Yoshida (2005), we show strong convergence for an accelerated Euler-Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result. The theoretical results …
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48 results for “Milstein scheme”
Neural networks estimate SDEs with jump noise using a Tamed-Milstein scheme.
problem Estimating drift and diffusion functions in SDEs with jump noise.
method Tamed-Milstein scheme with neural networks as non-parametric approximators.
result Flexible estimation of complex nonlinear dynamics in systems with state-dependent noise.
Develops numerical methods for pricing exchange options in a market with limited liquidity.
problem Pricing European style exchange options in a market with finite liquidity.
method Integrates price impact into the dynamics of correlated assets using a controlled variate approach.
result Numerical pricing methods for exchange options are developed and validated.
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.
In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth. Using Itô's formula, we get rid, in the asset price dynamics, of the stochastic i…
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milst…
New methods estimate Asian option prices more efficiently.
problem Estimating the price of discretely monitored Asian options.
method General multilevel Monte Carlo methods.
result Estimates with standard deviation in expected time.
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in the timestep and second order in the spatial gri…
GPU speeds up derivatives sensitivity computation for Heston model options.
problem Efficient computation of option Greeks under the Heston model.
method Implemented exact simulation and novel Milstein discretisation methods on GPU.
result GPU speeds up Greeks computation up to 200x compared to CPU methods.
Study compares models for pricing multi-strike quanto call options with SV, SC, and SER.
problem Pricing multi-strike quanto call options with stochastic volatility, correlation, and exchange rates.
method Comparative analysis of SV, SC, and SER models; Monte Carlo simulation; Milstein scheme; antithetic variates; correlation risk parameters.
result GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER model combination performs best.
GANs can approximate SDEs for large time steps.
problem Approximating SDEs for large time steps using GANs.
method Proposed a conditional GAN architecture to enable strong approximation of SDEs.
result Supervised GAN outperformed standard GAN and other schemes in strong error.
Pricing of European basket call option with n-assets and a bond is discussed in this paper, where all prices of n-assets and the bond are driven by Exponential Ornstein-Uhlenbeck processes. The close-form of European basket option pricing formula is derived. Utilizing with 1-order differential approximate numerical sol…
Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidenceq-fin.PM
The study extends SPT to account for real-world transaction costs, improving portfolio performance.
problem Real-world transaction costs affect portfolio performance, especially during market stress.
method Developed a continuous-time model with stochastic transaction costs and derived lower bounds for cost-adjusted wealth.
result Functionally generated portfolios can still achieve relative arbitrage after accounting for transaction costs.
Improved MLMC method for robust and efficient probability and density estimation.
problem Stability and poor complexity of MLMC for low-regularity functionals.
method Numerical smoothing combined with MLMC for deterministic quadrature methods.
result Significant improvement in strong convergence and robustness of MLMC method.
We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. I…
Study applies financial models to predict COVID-19 pandemic.
problem Predicting the spread of COVID-19 using financial market models.
method Implemented ARIMAX and Cox-Ingersoll-Ross (CIR) models, using Euler-Maruyama and Milstein methods for CIR*.
result CIR* framework provides accurate forecasts for pandemics.
We examine a general multi-factor model for commodity spot prices and futures valuation. We extend the multi-factor long-short model in Schwartz and Smith (2000) and Yan (2002) in two important aspects: firstly we allow for both the long and short term dynamic factors to be mean reverting incorporating stochastic volat…
Quantum algorithms speed up derivative pricing beyond Black-Scholes models.
problem Quantum speedups for derivative pricing beyond Black-Scholes models.
method Utilizing fast-forwardability and quantum Milstein sampler for non-GBM models, and improved numerical integration for GBM and CIR models.
result Quadratic speedups for derivative pricing in practical models like CIR and Heston's model.
New high-order scheme reduces BSDE truncation errors.
problem Numerical solution of backward stochastic differential equations (BSDEs).
method Proposes a new -scheme with careful 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…
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.
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.
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.
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.
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.
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 -schemes with finitely generated rings.
result Vector fields on affine -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 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.
Enhancing Efficiency of Pension Schemes through Effective Risk Governance: A Kenyan Perspectiveq-fin.RM
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 -stationary point within 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 -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.