SZodixStudyAcademic Library
ShelvesOpen access
Study · an open academic library·Metadata from OpenAlex (CC0)·Shelves·OpenAlex metadata, de-duplicated
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
16 references·0 citing·37 second hopsampled
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities (2020)Multilevel Picard approximations for high…Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations (2024)Local Lipschitz Continuity in…Deep Curve-Dependent PDEs for Affine Rough Volatility (2023)Deep Curve-Dependent PDEs for…Solving high-dimensional optimal stopping problems using deep learning (2021)Solving high-dimensional opti…On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations (2021)On nonlinear Feynman–Kac form…Multilevel Picard iterations for solving smooth semilinear parabolic heat equations (2021)Multilevel Picard iterations …Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems (2020)Rectified deep neural network…Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations (2020)Overcoming the curse of dimen…Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks (2020)Overcoming the curse of dimen…On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients (2020)On a perturbation theory and …Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions (2020)Deep neural network framework…Convergence of the deep BSDE method for coupled FBSDEs (2020)Convergence of the deep BSDE …On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations (2019)On Multilevel Picard Numerica…Deep optimal stopping (2018)Deep optimal stoppingDeep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM (2017)Deep Primal-Dual Algorithm fo…Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High Dimensional BSDEs (2017)Asymptotic Expansion as Prior…Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients (2014)Numerical approximations of s…A Theory of the Term Structure of Interest Rates (1985)A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993)A note on tamed Euler approximations (2013)Euler approximations with varying coefficients: The case of superlinearly growing diffusion coefficients (2016)Numerical solution of stochastic differential equations (2016)A Concise Course on Stochastic Partial Differential Equations (2007)Multilevel Monte Carlo Path Simulation (2008)Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients (2010)On stochastic differential equations with arbitrary slow convergence rates for strong approximation (2016)Adapted solution of a backward stochastic differential equation (1990)Backward Stochastic Differential Equations in Finance (1997)Reflected solutions of backward SDE's, and related obstacle problems for PDE's (1997)Forward-Backward Stochastic Differential Equations and their Applications (2007)A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks (1994)Valuing American Options by Simulation: A Simple Least-Squares Approach (2001)Monte Carlo valuation of American options (2002)Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications (2018)Fractional Brownian Motions, Fractional Noises and Applications (1968)Monte Carlo Methods in Financial Engineering (2003)Deep reinforcement learning for market making in corporate bonds: beating the curse of dimensionality (2019)Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space (2021)Solving forward-backward stochastic differential equations explicitly — a four step scheme (1994)Backward stochastic differential equations and quasilinear parabolic partial differential equations (2005)Three Algorithms for Solving High-Dimensional Fully Coupled FBSDEs Through Deep Learning (2020)Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games I: The Ergodic Case (2021)Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games: II—the finite horizon case (2022)Brownian Motion and Stochastic Calculus (2007)Numerical methods for backward stochastic differential equations: A survey (2023)Pricing American-style securities using simulation (1997)Stochastic Differential Equations (2003)Financial option valuation by unsupervised learning with artificial neural networks (2021)Deep stochastic optimization in finance (2022)Stochastic Differential Equations and Applications (1975)Hybrid Switching Diffusions (2009)Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients (2012)Deep xVA Solver – A Neural Network Based Counterparty Credit Risk Management Framework (2020)Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models (2021)
this work references cited by second hop· second hop is a sample of the most-cited connections

References

  • 2014Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients227 cited
  • 2018Deep optimal stopping138 cited
  • 2019On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations134 cited
  • 2020Convergence of the deep BSDE method for coupled FBSDEs134 cited
  • 2020On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients128 cited
  • 2017Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High Dimensional BSDEs91 cited
  • 2021Solving high-dimensional optimal stopping problems using deep learning88 cited
  • 2017Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM74 cited
  • 2021Multilevel Picard iterations for solving smooth semilinear parabolic heat equations69 cited
  • 2020Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems69 cited
  • 2020Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions63 cited
  • 2024Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations52 cited
  • 2020Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks

Only edges whose both ends are imported exist here. Widen the year window, or show the whole map. Back to the work

52 cited
  • 2020Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations50 cited
  • 2023Deep Curve-Dependent PDEs for Affine Rough Volatility33 cited
  • 2021On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations31 cited
  • Cited by

    No citing works inside the corpus for this window.