An efficient numerical method for forward-backward stochastic differential equations driven by \(G\)-Brownian motion

DOI10.1016/j.apnum.2021.03.012zbMath1484.65012arXiv2010.00253OpenAlexW3138871999WikidataQ115360342 ScholiaQ115360342MaRDI QIDQ2029145

Ming Shang Hu, Lianzi Jiang

Publication date: 3 June 2021

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.00253

zbMATH Keywords

numerical schemesbackward stochastic differential equationsfully nonlinear PDEs\(G\)-Brownian motion

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Numerical solutions to stochastic differential and integral equations (65C30) Nonlinear processes (e.g., (G)-Brownian motion, (G)-Lévy processes) (60G65)

Related Items (5)

Discrete‐time approximation for stochastic optimal control problems under the G‐expectation framework ⋮ Numerical methods for backward stochastic differential equations: a survey ⋮ Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations ⋮ An averaging principle for nonlinear parabolic PDEs via FBSDEs driven by \(G\)-Brownian motion ⋮ Pathwise convergence under Knightian uncertainty

Cites Work

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• Numerical Fourier method and second-order Taylor scheme for backward SDEs in finance
• Numerical simulations for \(G\)-Brownian motion
• Numerical schemes for \(G\)-expectations
• Wellposedness of second order backward SDEs
• Function spaces and capacity related to a sublinear expectation: application to \(G\)-Brownian motion paths
• A probabilistic numerical method for fully nonlinear parabolic PDEs
• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• Filtration consistent nonlinear expectations and evaluations of contingent claims
• Explicit solutions of the \(G\)-heat equation for a class of initial conditions
• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• On representation theorem of \(G\)-expectations and paths of \(G\)-Brownian motion
• A numerical scheme for BSDEs
• Discretizing a backward stochastic differential equation
• A multi-step scheme based on cubic spline for solving backward stochastic differential equations
• A monotone scheme for high-dimensional fully nonlinear PDEs
• Backward stochastic differential equations driven by \(G\)-Brownian motion
• Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by \(G\)-Brownian motion
• Second order discretization of backward SDEs and simulation with the cubature method
• A forward scheme for backward SDEs
• Representations and regularities for solutions to BSDEs with reflections
• Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation
• A regression-based Monte Carlo method to solve backward stochastic differential equations
• Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions
• Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
• Pricing and hedging derivative securities in markets with uncertain volatilities
• Uncertain volatility and the risk-free synthesis of derivatives
• Nonlinear Expectations and Stochastic Calculus under Uncertainty
• Linear Multistep Schemes for BSDEs
• Numerical Stability Analysis of the Euler Scheme for BSDEs
• A New Kind of Accurate Numerical Method for Backward Stochastic Differential Equations
• Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs
• Numerical Algorithms for Forward-Backward Stochastic Differential Equations

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