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On viscosity solutions of path dependent PDEs
13 references·16 citing·28 second hop
On viscosity solutions of path dependent PDEs (2014)On viscosity solutions of path dependent …Functional Itô calculus (2019)Functional Itô calculusFunctional Itô calculus and stochastic integral representation of martingales (2013)Functional Itô calculus and s…Wellposedness of second order backward SDEs (2011)Wellposedness of second order…Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs (2006)Second‐order backward stochas…Controlled Markov Processes and Viscosity Solutions (2005)Controlled Markov Processes a…Backward stochastic differential equations and quasilinear parabolic partial differential equations (2005)Backward stochastic different…Hedging and Portfolio Optimization in Financial Markets with a Large Trader (2003)Hedging and Portfolio Optimiz…Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type (1999)Monotonic limit theorem of BS…Forward-backward stochastic differential equations and quasilinear parabolic PDEs (1999)Forward-backward stochastic d…Reflected solutions of backward SDE's, and related obstacle problems for PDE's (1997)Reflected solutions of backwa…Backward Stochastic Differential Equations in Finance (1997)Backward Stochastic Different…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…Viscosity solutions to parabolic master equations and McKean–Vlasov SDEs with closed-loop controls (2020)Viscosity solutions to parabo…Branching diffusion representation of semilinear PDEs and Monte Carlo approximation (2019)Branching diffusion represent…Backward stochastic Volterra integral equations—Representation of adapted solutions (2019)Backward stochastic Volterra …A martingale approach for fractional Brownian motions and related path dependent PDEs (2019)A martingale approach for fra…Viscosity Solutions 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solve backward stochastic differential equations (2005)Continuous Martingales and Brownian Motion (1999)Stochastic Differential Equations (2014)Theory of Rational Option Pricing (1973)Filtration-consistent nonlinear expectations and related g-expectations (2002)Nonlinear Expectations, Nonlinear Evaluations and Risk Measures (2004)Theory of rational option pricing (2005)Backward stochastic differential equations with jumps and related non-linear expectations (2006)MULTI-DIMENSIONAL DIFFUSION PROCESSES (1980)Martingale representation theorem for the G -expectation (2010)Ambiguous Volatility and Asset Pricing in Continuous Time (2013)Martingale optimal transport and robust hedging in continuous time (2013)Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework (2000)On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case (2002)Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations (2019)Partial Differential Equations (2010)Change of variable formulas for non-anticipative functionals on path space (2010)
this work references cited by second hop

References

  • 2005Controlled Markov Processes and Viscosity Solutions2,698 cited
  • 1990Adapted solution of a backward stochastic differential equation2,676 cited
  • 1997Backward Stochastic Differential Equations in Finance2,339 cited
  • 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations782 cited
  • 1994Solving forward-backward stochastic differential equations explicitly — a four step scheme740 cited
  • 1997Reflected solutions of backward SDE's, and related obstacle problems for PDE's704 cited
  • 1999Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type347 cited
  • 1999Forward-backward stochastic differential equations and quasilinear parabolic PDEs329 cited
  • 2011Wellposedness of second order backward SDEs289 cited
  • 2019Functional Itô calculus257 cited
  • 2013Functional Itô calculus and stochastic integral representation of martingales252 cited
  • 2006Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs239 cited
  • 2003Hedging and Portfolio Optimization in Financial Markets with a Large Trader226 cited

Cited by

  • 2016Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II156 cited

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  • 2013Backward stochastic differential equations driven by G -Brownian motion148 cited
  • 2017Dynamic programming approach to principal–agent problems126 cited
  • 2016Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part I119 cited
  • 2014Two Person Zero-Sum Game in Weak Formulation and Path Dependent Bellman--Isaacs Equation107 cited
  • 2013A numerical algorithm for a class of BSDEs via the branching process99 cited
  • 2015BSDE, path-dependent PDE and nonlinear Feynman-Kac formula83 cited
  • 2019Branching diffusion representation of semilinear PDEs and Monte Carlo approximation82 cited
  • 2014Optimal stopping under nonlinear expectation78 cited
  • 2015Stochastic control for a class of nonlinear kernels and applications59 cited
  • 2020Viscosity solutions to parabolic master equations and McKean–Vlasov SDEs with closed-loop controls49 cited
  • 2018Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations44 cited
  • 2015Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations44 cited
  • 2011Note on Viscosity Solution of Path-Dependent PDE and G-Martingales44 cited
  • 2019A martingale approach for fractional Brownian motions and related path dependent PDEs42 cited
  • 2019Backward stochastic Volterra integral equations—Representation of adapted solutions42 cited