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Malliavin calculus for backward stochastic differential equations and application to numerical solutions
15 references·9 citing·24 second hop
Malliavin calculus for backward stochastic differential equations and application to numerical solutions (2016)Malliavin calculus for backward stochasti…Backward Stochastic Differential Equations (2013)Backward Stochastic Different…Path regularity and explicit convergence rate for BSDE with truncated quadratic growth (2009)Path regularity and explicit …Forward-Backward Stochastic Differential Equations and their Applications (2007)Forward-Backward Stochastic D…A forward scheme for backward SDEs (2007)A forward scheme for backward…The Malliavin Calculus and Related Topics (2006)The Malliavin Calculus and Re…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 BSDEsNumberical Method for Backward Stochastic Differential Equations (2002)Numberical Method for Backwar…Donsker-Type Theorem for BSDEs (2001)Donsker-Type Theorem for BSDEsForward-Backward Stochastic Differential Equations and Their Applications (1999)Forward-Backward Stochastic D…Backward Stochastic Differential Equations in Finance (1997)Backward Stochastic Different…The Malliavin Calculus and Related Topics (1995)The Malliavin Calculus and Re…Solving forward-backward stochastic differential equations explicitly — a four step scheme (1994)Solving forward-backward stoc…Adapted solution of a backward stochastic differential equation (1990)Adapted solution of a backwar…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 f…Linear Volterra backward stochastic integral equations (2018)Linear Volterra backward stoc…Singular mean-field control games (2017)Singular mean-field control g…Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering (2017)Improved error bounds for qua…Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations (2016)Adaptive importance sampling …Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression (2015)Approximation of backward sto…Monotone schemes for fully nonlinear parabolic path dependent PDEs (2014)Monotone schemes for fully no…BSDEs with terminal conditions that have bounded Malliavin derivative (2013)BSDEs with terminal condition…Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions (2012)Maximum Principle for General…Valuing American Options by Simulation: A Simple Least-Squares Approach (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)Controlled Diffusion Processes (1980)Stochastic Integration and Differential Equations (1990)Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control (1999)Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework (2000)Backward stochastic differential equations and quasilinear parabolic partial differential equations (2005)Brownian Motion and Stochastic Calculus (2007)Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations (2006)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)Applications of Malliavin calculus to Monte Carlo methods in finance (1999)Stochastic Calculus with Respect to Gaussian Processes (2001)Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Central limit theorems for sequences of multiple stochastic integrals (2005)Relationship Between Backward Stochastic Differential Equations and Stochastic Controls: A Linear-Quadratic Approach (2000)Backward Stochastic Differential Equations and Feynman-Kac Formula for Levy Processes, with Applications in Finance (2001)A Leader-Follower Stochastic Linear Quadratic Differential Game (2002)Stochastic Differential Equations (2014)
this work references cited by second hop

References

  • 1990Adapted solution of a backward stochastic differential equation2,676 cited
  • 2006The Malliavin Calculus and Related Topics2,470 cited
  • 1997Backward Stochastic Differential Equations in Finance2,339 cited
  • 1995The Malliavin Calculus and Related Topics1,545 cited
  • 1994Solving forward-backward stochastic differential equations explicitly — a four step scheme740 cited
  • 2007Forward-Backward Stochastic Differential Equations and their Applications675 cited
  • 2004Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations518 cited
  • 2005A regression-based Monte Carlo method to solve backward stochastic differential equations412 cited
  • 2004A numerical scheme for BSDEs371 cited
  • 1999Forward-Backward Stochastic Differential Equations and Their Applications258 cited
  • 2007A forward scheme for backward SDEs186 cited
  • 2013Backward Stochastic Differential Equations159 cited
  • 2002Numberical Method for Backward Stochastic Differential Equations154 cited
  • 2001Donsker-Type Theorem for BSDEs108 cited
  • 2009Path regularity and explicit convergence rate for BSDE with truncated quadratic growth64 cited

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Cited by

  • 2013BSDEs with terminal conditions that have bounded Malliavin derivative46 cited
  • 2015Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression42 cited
  • 2018Linear Volterra backward stochastic integral equations30 cited
  • 2017Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering28 cited
  • 2012Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions27 cited
  • 2016Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations26 cited
  • 2017Singular mean-field control games24 cited
  • 2014Monotone schemes for fully nonlinear parabolic path dependent PDEs23 cited
  • 2021Strong 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 equation20 cited