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.
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…
We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at fixed dates. Our approach yields unbiased estimators with standard deviation in expected time for a variety of processes including the Black-Scholes model, Merton's jump-diffusion mod…
Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large derivative books. Recursive Marginal Quantization of the Euler scheme has recen…
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…
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.
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…
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.
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 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.
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.
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 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.
We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization schemes: an explicit Euler scheme, an implicit Euler scheme, and a symplectic scheme.…
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.
In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional -scheme, we reduce truncation errors by taking carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear…
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.
We extend the scheme developed in B. Düring, A. Pitkin, "High-order compact finite difference scheme for option pricing in stochastic volatility jump models", 2019, to the so-called stochastic volatility with contemporaneous jumps (SVCJ) model, derived by Duffie, Pan and Singleton. The performance of the scheme is asse…
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.
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.
In this paper we propose a generalized numerical scheme for backward stochastic differential equations(BSDEs). The scheme is based on approximation of derivatives via Lagrange interpolation. By changing the distribution of sample points used for interpolation, one can get various numerical schemes with different stabil…
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 this paper, we propose an acceleration scheme for online memory-limited PCA methods. Our scheme converges to the first eigenvectors in a single data pass. We provide empirical convergence results of our scheme based on the spiked covariance model. Our scheme does not require any predefined parameters such as t…
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.
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 …
We present a new high-order compact scheme for the multi-dimensional Black-Scholes model with application to European Put options on a basket of two underlying assets. The scheme is second-order accurate in time and fourth-order accurate in space. Numerical examples confirm that a standard second-order finite differenc…
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.
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 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…