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A monotone scheme for high-dimensional fully nonlinear PDEs
16 references·7 citing·32 second hopsampled
A monotone scheme for high-dimensional fully nonlinear PDEs (2015)A monotone scheme for high-dimensional fu…Nonlinear Expectations and Stochastic Calculus under Uncertainty (2019)Nonlinear Expectations and St…Wellposedness of second order backward SDEs (2011)Wellposedness of second order…A probabilistic numerical method for fully nonlinear parabolic PDEs (2011)A probabilistic numerical met…A forward scheme for backward SDEs (2007)A forward scheme for backward…Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs (2006)Second‐order backward stochas…A forward–backward stochastic algorithm for quasi-linear PDEs (2006)A forward–backward stochastic…Backward stochastic differential equations and quasilinear parabolic partial differential equations (2005)Backward stochastic different…A regression-based Monte Carlo method to solve backward stochastic differential equations (2005)A regression-based Monte Carl…A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS (2005)A QUANTIZATION TREE METHOD FO…Number of paths versus number of basis functions in American option pricing (2004)Number of paths versus number…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 BSDEsAn analysis of a least squares regression method for American option pricing (2002)An analysis of a least square…Valuing American Options by Simulation: A Simple Least-Squares Approach (2001)Valuing American Options by S…Numerical methods for forward-backward stochastic differential equations (1996)Numerical methods for forward…Solving forward-backward stochastic differential equations explicitly — a four step scheme (1994)Solving forward-backward stoc…Numerical methods for backward stochastic differential equations: A survey (2023)Numerical methods for backwar…Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks (2020)Overcoming the curse of dimen…High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control (2017)High Order Numerical Schemes …Efficient spectral sparse grid approximations for solving multi-dimensional forward backward SDEs (2017)Efficient spectral sparse gri…Numerical simulations for G-Brownian motion (2016)Numerical simulations for G-B…Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps (2015)Discrete time approximation o…A complete representation theorem for G-martingales (2014)A complete representation the…Brownian Motion and Stochastic Calculus (1988)Adapted solution of a backward stochastic differential equation (1990)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)Brownian Motion and Stochastic Calculus (2007)Backward Stochastic Differential Equations in Finance (1997)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)Pricing American-style securities using simulation (1997)Regression methods for pricing complex American-style options (2001)A Monte Carlo Method for Optimal Portfolios (2003)OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS (2008)Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations (2006)Numerical solution of stochastic differential equations (2016)Coherent Measures of Risk (1999)Continuous Martingales and Brownian Motion (1999)Ambiguous Volatility and Asset Pricing in Continuous Time (2013)Arbitrage and duality in nondominated discrete-time models (2015)The Pricing of Options and Corporate Liabilities (1973)Theory of Rational Option Pricing (1973)New frontiers for arch models (2002)Option Pricing Under a Double Exponential Jump Diffusion Model (2004)Theory of rational option pricing (2005)Stochastic Differential Equations and Diffusion Processes (1983)Monte Carlo Methods in Financial Engineering (2003)Stochastic Differential Games and Viscosity Solutions of Hamilton–Jacobi–Bellman–Isaacs Equations (2008)Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations (2009)Martingale representation theorem for the G -expectation (2010)MULTI-DIMENSIONAL DIFFUSION PROCESSES (1980)Martingale optimal transport and robust hedging in continuous time (2013)
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References

  • 2001Valuing American Options by Simulation: A Simple Least-Squares Approach3,218 cited
  • 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations782 cited
  • 1994Solving forward-backward stochastic differential equations explicitly — a four step scheme740 cited
  • 2019Nonlinear Expectations and Stochastic Calculus under Uncertainty594 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
  • 2002An analysis of a least squares regression method for American option pricing342 cited
  • 2011Wellposedness of second order backward SDEs289 cited
  • 2006Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs239 cited
  • 2005A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS192 cited
  • 2007A forward scheme for backward SDEs186 cited
  • 1996Numerical methods for forward-backward stochastic differential equations181 cited
  • 2011A probabilistic numerical method for fully nonlinear parabolic PDEs167 cited

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2004
Number of paths versus number of basis functions in American option pricing
151 cited
  • 2006A forward–backward stochastic algorithm for quasi-linear PDEs136 cited
  • Cited by

    • 2020Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks52 cited
    • 2015Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps46 cited
    • 2014A complete representation theorem for G-martingales41 cited
    • 2017Efficient spectral sparse grid approximations for solving multi-dimensional forward backward SDEs37 cited
    • 2017High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control36 cited
    • 2023Numerical methods for backward stochastic differential equations: A survey32 cited
    • 2016Numerical simulations for G-Brownian motion31 cited