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 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.
Efficiently prices options in stochastic volatility models using sparse grids.
problem Option pricing in stochastic volatility models.
method Sparse grid high-order ADI scheme for second-order in time and fourth-order in space.
result Computational efficiency gains confirmed by numerical experiments.
A new averaging scheme improves stochastic gradient methods.
problem Improving the performance of stochastic gradient descent.
method Proposes a weighted averaging scheme with decaying weights.
result The method has a regularizing effect equivalent to ridge regression.
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. 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.
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.
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.
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.
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 paper uses potential functions to help reinforcement learning agents learn optimal policies.
problem Learning optimal stochastic policies in reinforcement learning.
method Augmenting the reward with potential functions and applying these to policy gradient algorithms.
result Potential-based reward shaping preserves optimality of stochastic policies and speeds up learning.
New approach connects stochastic gradient descent to ODE splitting schemes.
problem Improving convergence in stochastic optimization.
method Connection between stochastic gradient descent and ODE splitting schemes.
result Derive a new upper bound on global splitting error.
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Lévy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Lévy process with a high order scheme for the Brownian driven component, applied bet…
We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for asymptotic optimality of standard stochastic gradient procedures. Roughly, the n…
Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.
problem Improving convergence of SGD in various settings.
method Develops a general weighted averaging scheme for SGD and establishes asymptotic normality.
result Establishes asymptotic normality and optimality of weighted averaged SGD solutions.
We study the Heston-Cox-Ingersoll-Ross++ stochastic-local volatility model in the context of foreign exchange markets and propose a Monte Carlo simulation scheme which combines the full truncation Euler scheme for the stochastic volatility component and the stochastic domestic and foreign short interest rates with the …
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…
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…
The paper analyzes Euler approximations for complex volatility models with strong convergence rates.
problem Analyzing strong convergence rates for Euler approximations in stochastic path-dependent volatility models.
method Proposes a Monte Carlo simulation scheme combining log-Euler and truncation/Euler-Maruyama schemes.
result Establishes strong convergence rate of 1/2 for the approximation process up to a critical time.
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …
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 …
The paper analyzes fixed step-size SA schemes on Riemannian manifolds.
problem Developing efficient algorithms for optimization on curved spaces.
method Fixed step-size stochastic approximation schemes in a Riemannian framework.
result The schemes converge to the solution as the step-size approaches zero.
The paper models FX option skew using SLV models with stochastic correlation and jumps.
problem Stochastic skew of FX options.
method Created SLV models with stochastic correlation and jumps, using Levy processes for drivers and a new finite-difference scheme for calibration.
result Demonstrated capacity of the model in modeling stochastic skew.
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.
We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero …
Simplified SGD interpretation as Ito process for broader applicability.
problem Lack of generality in current SGD interpretation.
method Introduced a simplified scheme for discrete-time approximation of Ito process.
result Flexibly interprets SGD and SGLD, providing insights into their asymptotic properties.
Efficiently simulates the Heston model with large time steps using a novel method.
problem Challenges in simulating the Heston model with large time steps.
method Implicit integrated variance scheme exploiting the near-linear nature between stochastic driver and conditional integrated variance process.
result Achieves near-exact accuracy with coarse discretizations, efficient for large time steps.
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.
Study on improving the linear two-time-scale stochastic approximation method with a restarting scheme.
problem Characterizing and optimizing the finite-time complexity of linear two-time-scale stochastic approximation.
method Analysis of mean square errors, introduction of a restarting scheme to improve performance.
result The method achieves an exact convergence to the desired solution with improved complexity under time-varying step sizes.
GPU speeds up Monte Carlo simulations for large time steps.
problem Slow convergence and inaccurate solutions with large time steps in Monte Carlo simulations.
method Generalizes the Seven League scheme for GPU acceleration.
result Significantly improved computational speed.
New method for pricing options in stochastic volatility models.
problem Pricing options in models with stochastic volatility.
method Time-adaptive, high-order compact finite difference scheme.
result Extends fourth-order multistep methods to stochastic volatility models.
A new machine learning method solves high-dimensional Kolmogorov PDEs efficiently.
problem Solving high-dimensional Kolmogorov PDEs and SDEs.
method Stochastic weighted minimization and stochastic gradient descent with Malliavin weights.
result Accurate approximation of high-dimensional Kolmogorov PDEs and SDEs without curse of dimensionality.
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.
Improved multilevel scheme for value-at-risk computation.
problem Discontinuity in Heaviside function affects value-at-risk computation.
method Adaptive multilevel stochastic approximation to mitigate discontinuity.
result Best complexity improved to O( ε − 2 ∣ ln ε ∣ 5 2 \varepsilon^{-2}|\ln{\varepsilon}|^\frac52 ε − 2 ∣ ln ε ∣ 2 5 ). Gradient descent stagnates in low-precision, but unbiased rounding schemes improve convergence.
problem Stagnation of gradient descent in low-precision computation.
method Proposed unbiased stochastic rounding schemes that trade zero bias for larger probability of preserving small gradients.
result Unbiased rounding methods typically improve convergence rate of gradient descent for convex problems.
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results like unconditional stability in the sense of von Neumann are presented. Where the a…
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.
A new fast method simulates stochastic volatility models.
problem Simulating stochastic volatility models efficiently.
method Karhunen-Loève expansions to express stochastic volatility as sine series, followed by analytical derivation of integrals.
result Simulation is several hundred times faster than existing methods.
New algorithm improves convergence rates for convex optimization problems.
problem Convex optimization problems with noisy stochastic data.
method Stochastic proximal point algorithm with weak linear regularity condition.
result Achieves $\mathcal{O}\left(\frac{1}{k}
ight)$ convergence rate for SPP.
Deep learning scheme identifies and reconstructs chaotic and stochastic systems from noisy data.
problem Challenging identification of governing equations from noisy and partial observations.
method Jointly learns inference model and governing laws using variational deep learning.
result Framework generalizes state-of-the-art methods and accounts for stochastic variabilities.
Deep learning accelerates Monte Carlo SDE simulations with large time steps.
problem Accurate simulation of SDEs with large time steps.
method Polynomial chaos expansion with neural network learned stochastic collocation points.
result Data-driven scheme achieves strong convergence in Monte Carlo simulations.
Develops multifactor approximations for SVEs with completely monotone kernels.
problem Approximating SVEs with kernels of completely monotone type.
method Multifactor approximation, Euler discretization, L 2 L^2 L 2 -estimation, convergence analysis. result New multifactor Euler scheme reduces computational cost and outperforms SVEs for option pricing.
Study simulates Heston-type local stochastic volatility model using particle method.
problem Simulate calibrated Heston-type local stochastic volatility model with non-standard coefficients.
method Monte Carlo particle method, Euler-Maruyama scheme, full truncation Euler scheme.
result Strong convergence of Euler-Maruyama scheme with rate 1/2 in time, up to a logarithmic factor.
Paper develops Euler scheme for fractional delay diff. eqs with additive noise.
problem Developing a consistent Euler-Maruyama scheme for fractional stochastic delay diff. eqs.
method Euler-Maruyama scheme for fractional Brownian motion with additive noise.
result Achieved convergence rate of H+1/2 for smooth delays when H>1/2.
Developed unbiased estimators for Heston model with stochastic interest rates.
problem Estimating the Heston model with stochastic interest rates.
method Combined unbiased estimators with the Heston model and developed a semi-exact log-Euler scheme.
result Convergence rate of O ( h ) O(h) O ( h ) in the L 2 L^2 L 2 norm for a wide range of models. New method bounds stochastic subgradient methods with heavy-tailed noise.
problem Bounding stochastic subgradient methods under heavy-tailed noise.
method Clipped version of projected stochastic subgradient method.
result Near optimal any-time and finite horizon bounds for averaging schemes.
RELTA-SGLD stabilizes nonconvex SGLD updates with a lighter taming scheme.
problem Stabilizing superlinear stochastic-gradient updates in nonconvex optimization.
method Threshold-based taming with relative-growth principle for stability.
result Polynomial moment stability and first-order stationary accuracy in nonconvex SGLD.
We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to deal with the …