We demonstrate that the use of asymptotic expansion as prior knowledge in the "deep BSDE solver", which is a deep learning method for high dimensional BSDEs proposed by Weinan E, Han & Jentzen (2017), drastically reduces the loss function and accelerates the speed of convergence. We illustrate the technique and its imp…
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48 results for “Deep BSDE solver”
Deep learning method improves numerical approximation of FBSDEs with jumps.
problem Improving numerical solutions for FBSDEs with jumps.
method Deep learning-based approach for decoupled FBSDEs with jumps.
result A priori and a posteriori error estimates for finite and infinite activity cases.
Paper introduces a new method to solve complex PDEs efficiently.
problem Solving high-dimensional semilinear PDEs and BSDEs.
method Decomposes PDEs into linear and nonlinear parts, uses Deep BSDE solver with control variate method.
result Errors of the new method are much smaller than those of the original Deep BSDE solver.
KANHedge improves hedging of high-dimensional options using learnable B-spline activation functions.
problem Challenges in high-dimensional option pricing and hedging due to the curse of dimensionality.
method Introduces KANHedge, a novel BSDE-based hedger leveraging Kolmogorov-Arnold Networks with learnable B-spline activation functions.
result KANHedge provides improved hedging performance, achieving significant reductions in hedging cost metrics.
New integration method improves BSDE-based PDE solvers.
problem Discretization bias in standard BSDE-based solvers.
method Proposed Stratonovich-based BSDE formulation with stochastic Heun integration.
result Eliminates bias issues and outperforms EM-based variants.
Quantum machine learning solves high-dimensional PDEs with lower variance and improved accuracy.
problem Approximating solutions to high-dimensional parabolic PDEs.
method Pure Variational Quantum Circuit (VQC) for BSDE approximation, using temporal discretization and Monte Carlo simulation.
result VQC achieves lower variance and improved accuracy in most cases, particularly in highly nonlinear regimes.
Paper presents a neural network method for efficient xVA computation and risk management.
problem High-dimensional counterparty credit risk valuation and management.
method Neural network-based BSDE solver for coupled system of BSDEs for xVA.
result Efficient computation of xVA for high-dimensional portfolios.
Deep Quadratic Hedgingq-fin.CP
Deep learning solves high-dimensional quadratic hedging problems.
problem High-dimensional incomplete markets with mean-variance and local risk minimization.
method Deep learning-based BSDE solver for optimal hedging strategies.
result High-dimensional quadratic hedging is efficiently computed with deep learning.
Extends deep solver to FBSDEs with jumps for option pricing.
problem Solving FBSDEs with jumps for financial applications.
method Discretization, ANN parametrization, reinforcement learning, loss function minimization.
result Successfully applied to option pricing in low and high dimensions.
Study evaluates Deep PDE solvers for high-dimensional option pricing, identifying key sources of error.
problem Empirical study on error analysis of Deep PDE solvers for high-dimensional option pricing.
method Comparative experiments with Deep BSDE method and other solvers, identifying three main sources of error.
result Deep BSDE method is superior and robust to option specifications, improving with larger batch sizes and fewer time steps.
Deep neural RDEs improve portfolio optimization accuracy and risk sensitivity.
problem High-dimensional, path-dependent valuation and control problems.
method Coupling truncated log-signatures with a neural RDE backbone.
result Improved accuracy, tail fidelity, and training stability across various financial models.
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
problem Nonlinear Forward Backward Stochastic Differential Equations (FBSDE) with terminal conditions.
method Backward deep BSDE method applied to FBSDE with nonlinear generators and random initial conditions.
result Derives exact and Taylor-based approximations for time-stepping nonlinear BSDEs.
A new deep generative model uses BSDEs for high-dimensional data generation.
problem Generating high-dimensional complex data, especially images.
method Combines BSDEs with deep neural networks for training with MMD loss.
result BSDE-Gen effectively generates high-dimensional data with stochasticity.
As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic differential equation (BSDE). We can either solve the PDE to obtain option prices or…
Novel filter uses deep BSDE for nonlinear density approximation.
problem Nonlinear filtering problem.
method Bayesian filter based on deep BSDE and neural networks.
result Theoretical convergence rate confirmed in numerical examples.
A new method solves complex financial problems using deep learning.
problem Optimal stopping and option pricing in finance.
method Compound BSDE method, based on reformulating BSDEs.
result The method offers accurate and efficient solutions for high-dimensional problems.
New algorithm solves complex equations using deep learning.
problem High-dimensional nonlinear PDEs and BSDEs.
method Iterated time discretization, deep neural networks, stochastic gradient descent.
result Increased accuracy and reduced complexity compared to existing methods.
A new algorithm solves high-dimensional nonlinear BSDEs efficiently.
problem Solving high-dimensional nonlinear backward stochastic differential equations (BSDEs).
method Transformed BSDE into a differential deep learning problem using Malliavin calculus. Discretized integrals using Euler-Maruyama method. Approximated solution with three deep neural networks. Optimized parameters using a differential learning loss function.
result Our algorithm is more accurate and faster than other methods.
A new algorithm solves high-dimensional nonlinear BSDEs using deep learning.
problem Solving high-dimensional nonlinear backward stochastic differential equations (BSDEs).
method Backward differential deep learning, reformulating BSDEs as differential deep learning problems, using Malliavin calculus, discretizing integrals with Euler-Maruyama method, approximating processes with DNNs, backwardly optimizing DNN parameters.
result The proposed algorithm efficiently approximates solutions and their derivatives for high-dimensional BSDEs.
Deep BSDE method for pricing and hedging complex financial portfolios.
problem Simultaneous pricing and delta-gamma hedging of large portfolios of multi-asset Bermudan options.
method Discretely reflected BSDEs, One Step Malliavin scheme, neural network regression Monte Carlo method.
result Efficient and accurate pricing and hedging strategies for high-dimensional portfolios.
New deep learning method solves complex BSDEs efficiently.
problem Solving high-dimensional nonlinear BSDEs.
method Reformulate as global optimization, approximate solution with deep neural network, globally minimize quadratic local loss functions.
result Demonstrated effectiveness on various high-dimensional nonlinear BSDEs, including finance applications.
Two deep learning algorithms solve utility maximisation problems in finance.
problem Solving utility maximisation problems in finance with deep learning.
method Two algorithms: one for Markovian problems via HJB equation and 2BSDE, the other for non-Markovian problems via adjoint BSDE.
result Highly accurate results with low computational cost, solving problems with power, log, and non-HARA utilities in various models.
Unified approach combining BSDEs and PINNs for solving PDEs.
problem Solving high-dimensional partial differential equations.
method Interpolating between BSDEs and PINNs using diffusion loss.
result Unified understanding of numerical approaches for high-dimensional PDEs.
Paper proves deep learning method for stochastic control converges and outperforms existing algorithms.
problem Formulating and solving stochastic control problems using FBSDE and SMP.
method Deep learning algorithm based on SMP, with convergence proof and error bounds.
result Deep SMP-BSDE algorithm converges and outperforms existing methods in high-dimensional stochastic control problems.
New deep learning method solves stochastic control problems.
problem Solving strongly coupled FBSDEs for stochastic control.
method Modified deep BSDE method with new loss function.
result Empirical convergence of the new method for three problems.
A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion modelsq-fin.CP
New deep learning method for option pricing in jump-diffusion models.
problem Option pricing in jump-diffusion models with high-dimensional assets.
method Implicit-explicit minimizing movement time-stepping approach using deep ANNs.
result Consistent and asymptotically correct solutions for large underlyings.
We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function, and the loss functi…
The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives with Libor market models is mainly carried out with Monte Carlo simulation. The PDE…
Deep learning solves complex volatility equations.
problem Solving path-dependent PDEs in rough volatility.
method Interpreting PDE as BSDE, using neural network reservoir approach.
result Proved theoretical convergence for least-square regression.
End-to-end trainable graph matching using improved combinatorial solvers.
problem Graph matching in deep learning.
method Combining deep learning with optimized combinatorial solvers.
result Advances state-of-the-art on deep graph matching benchmarks.
Higher-order ODE solvers improve deep learning performance.
problem Improving deep learning performance using higher-order ODE solvers.
method Evaluation and improvement of Runge-Kutta (RK) methods for deep learning.
result Higher-order RK solvers can improve deep learning performance by incorporating key ingredients of optimizers.
New method tackles convergence issues in approximating FBSDEs.
problem Convergence issues in approximating coupled FBSDEs.
method Approximates initial condition for a family of FBSDEs, then uses it to approximate the original FBSDE.
result Method converges even when standard deep BSDE method fails.
A new method uses deep learning to price barrier options.
problem Pricing barrier options with boundary conditions.
method Forward deep BSDEs with added nodes for barrier conditions.
result Can handle any barrier condition and boundary conditions.
A deep BSDE approach tackles multi-layered xVA calculations for portfolio valuation.
problem Computational intractability in nested simulations for multi-layered xVA calculations.
method Iterative deep BSDE approach, change-of-measure method, quantile regression for margin computation.
result Reduces computational demands and successfully scales to high-dimensional portfolios.
We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonst…
This research analyzes deep PDE solvers for option pricing accuracy.
problem Understanding the accuracy of deep learning methods for solving PDEs in option pricing.
method Comparative experiments with two neural network algorithms in Black--Scholes and Heston models.
result Empirical convergence rates and training times of TDGF method determined.
The paper addresses XVA valuation under market crises using a renewal process.
problem XVA valuation without considering market crises and illiquidity.
method Using an alternating renewal process, the paper develops a framework to price XVA under a state-dependent financial regime.
result The XVA price is characterized as a solution to a backward stochastic differential equation (BSDE).
Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfoldingcond-mat.dis-nn
Deep unfolding accelerates MCMC-based COP solvers.
problem Optimizing combinatorial problems with MCMC and gradient descent.
method Combines MCMC and gradient descent, trains step sizes, uses variance estimation for non-differentiable MCMC.
result Significantly accelerates convergence speed for COPs.
Study uses G-BSDEs to decompose pricing kernels under robust G-expectation.
problem Long-term decomposition of robust pricing kernels under G-expectation.
method Proposes and analyzes three types of quadratic G-BSDEs to decompose pricing kernels.
result Pricing kernels decomposed into four components: discounting, transitory, symmetric martingale, and volatility uncertainty.
Deep learning model solves high-dimensional PDEs using Actor-Critic approach.
problem Solving high-dimensional nonlinear PDEs efficiently.
method Reformulated PDE into BSDE system, inspired by Actor-Critic algorithm for deep RL.
result Improved model with fewer parameters, faster convergence, and less hyperparameter tuning.
Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEsmath.PR
The paper tackles pricing vulnerable options via generalized BSDEs and penalization schemes.
problem Pricing options in a general hazard process setup.
method Establishes well-posedness and comparison theorems for generalized BSDEs and RBSDEs, studies penalization schemes.
result Well-posedness results and comparison theorems for generalized BSDEs and RBSDEs, extended penalization schemes.
Geometric BSDEsmath.PR
Develops geometric BSDEs for modeling dynamic return risk measures.
problem Modeling continuous-time dynamic return risk measures.
method Introduces and develops Geometric Backward Stochastic Differential Equations (GBSDEs) and two-driver BSDEs.
result Establishes existence, regularity, uniqueness, and stability of solutions to GBSDEs.
A new method uses deep learning for optimal stopping problems.
problem Solving optimal stopping problems in financial mathematics.
method Deep primal-dual BSDE framework with a novel loss function.
result The method provides a true upper bound for the optimal value.
Deep Penalty Method solves high-dimensional optimal stopping problems using deep learning.
problem High-dimensional optimal stopping problems in American option pricing.
method Inspired by penalty method for PDEs, approximates penalized PDE with Deep BSDE framework.
result Error bound of DPM is .
SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solvercs.LG
Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. …
Study on BSDEs with random time horizon, focusing on existence and properties.
problem Existence of solutions to BSDEs and reflected BSDEs with a random time horizon.
method Method of reduction and examination of BSDEs with lahdlaug driver.
result Existence of solutions to BSDEs and reflected BSDEs with a random time horizon.
New methods solve complex financial equations.
problem Solving backward stochastic differential equations driven by continuous-time Markov chains.
method Multi-stage Euler-Maruyama methods and multilevel spatial discretization.
result Efficiently solved stiff Markov BSDEs.
A new unsupervised learning method calibrates rough volatility models efficiently.
problem Efficient calibration of rough volatility models with minimal data.
method Unsupervised learning using BSDE representation and neural networks.
result The proposed scheme minimizes loss and approximates BSDE solution.