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Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat equation
16 references·0 citing·28 second hop
Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat equation (2021)Strong rates of convergence for a space-t…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…Malliavin calculus for backward stochastic differential equations and application to numerical solutions (2016)Malliavin calculus for backwa…Linear Multistep Schemes for BSDEs (2014)Linear Multistep Schemes for …General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions (2014)General Pontryagin-Type Stoch…Strong solution of backward stochastic partial differential equations in C 2 domains (2011)Strong solution of backward s…Malliavin calculus for backward stochastic differential equations and application to numerical solutions (2011)Malliavin calculus for backwa…Time discretization and Markovian iteration for coupled FBSDEs (2008)Time discretization and Marko…A forward scheme for backward SDEs (2007)A forward scheme for backward…Time discretization and Markovian iteration for coupled FBSDEs (2006)Time discretization and Marko…The Malliavin Calculus and Related Topics (2006)The Malliavin Calculus and Re…A New Kind of Accurate Numerical Method for Backward Stochastic Differential Equations (2006)A New Kind of Accurate Numeri…A regression-based Monte Carlo method to solve backward stochastic differential equations (2005)A regression-based Monte Carl…Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations (2004)Discrete-time approximation a…A numerical scheme for BSDEs (2004)A numerical scheme for BSDEsStochastic controls : Hamiltonian systems and HJB equations (1999)Stochastic controls : Hamilto…Backward Stochastic Differential Equations in Finance (1997)Backward Stochastic Different…Adapted solution of a backward stochastic differential equation (1990)Valuing American Options by Simulation: A Simple Least-Squares Approach (2001)A Stable Multistep Scheme for Solving Backward Stochastic Differential Equations (2010)Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011)New Kinds of High-Order Multistep Schemes for Coupled Forward Backward Stochastic Differential Equations (2014)Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations (2006)Brownian Motion and Stochastic Calculus (2007)Numerical solution of stochastic differential equations (2016)The Pricing of Options and Corporate Liabilities (1973)Reflected solutions of backward SDE's, and related obstacle problems for PDE's (1997)Backward stochastic differential equations and partial differential equations with quadratic growth (2000)Theory of rational option pricing (2005)Partial Differential Equations (2010)A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993)Monte Carlo Methods in Financial Engineering (2003)On Numerical Approximations of Forward-Backward Stochastic Differential Equations (2008)TRUE UPPER BOUNDS FOR BERMUDAN PRODUCTS VIA NON‐NESTED MONTE CARLO (2009)Least-Squares Monte Carlo for Backward SDEs (2012)Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework (2000)G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type (2007)Nonlinear Expectations and Stochastic Calculus under Uncertainty (2019)Applications of Malliavin calculus to Monte Carlo methods in finance (1999)Stochastic Calculus with Respect to Gaussian Processes (2001)Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs (2006)Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations (2019)Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High Dimensional BSDEs (2017)Convergence of the deep BSDE method for coupled FBSDEs (2020)Multilevel Picard iterations for solving smooth semilinear parabolic heat equations (2021)
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References

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  • 2007A forward scheme for backward SDEs186 cited
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  • 2019On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations134 cited
  • 2006Time discretization and Markovian iteration for coupled FBSDEs106 cited
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  • 2014General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions83 cited
  • 2014Linear Multistep Schemes for BSDEs65 cited
  • 2016Malliavin calculus for backward stochastic differential equations and application to numerical solutions53 cited

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  • 2011Strong solution of backward stochastic partial differential equations in C 2 domains50 cited
  • 2011Malliavin calculus for backward stochastic differential equations and application to numerical solutions45 cited
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