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BSDE, path-dependent PDE and nonlinear Feynman-Kac formula
16 references·15 citing·30 second hop
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and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths (2010)Nonlinear Expectations and Stochastic Calculus under Uncertainty (2019)Numerical solution of stochastic differential equations (2016)Theory of Rational Option Pricing (1973)Stochastic Differential Equations and Diffusion Processes (1983)A General Stochastic Maximum Principle for Optimal Control Problems (1990)Solution of forward-backward stochastic differential equations (1995)Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control (1999)Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework (2000)A numerical scheme for BSDEs (2004)Stochastic Differential Equations (2014)
this work references cited by second hop

References

  • 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
  • 2007Forward-Backward Stochastic Differential Equations and their Applications675 cited
  • 2007G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type621 cited
  • 2004Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations518 cited
  • 1991Probabilistic interpretation for systems of quasilinear parabolic partial differential equations518 cited
  • 2005A regression-based Monte Carlo method to solve backward stochastic differential equations412 cited
  • 2003Lp solutions of backward stochastic differential equations367 cited
  • 2019Functional Itô calculus257 cited
  • 2013Functional Itô calculus and stochastic integral representation of martingales252 cited
  • 1998Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order213 cited
  • 2014On viscosity solutions of path dependent PDEs181 cited
  • 1996Numerical methods for forward-backward stochastic differential equations181 cited

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  • 2010Change of variable formulas for non-anticipative functionals on path space172 cited
  • 2005NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS159 cited
  • Cited by

    • 2020Viscosity solutions to parabolic master equations and McKean–Vlasov SDEs with closed-loop controls49 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
    • 2017Theory, methods and meaning of nonlinear expectation theory40 cited
    • 2017Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs38 cited
    • 2016An infinite-dimensional approach to path-dependent Kolmogorov equations35 cited
    • 2016An infinite-dimensional approach to path-dependent Kolmogorov equations32 cited
    • 2020Extended backward stochastic Volterra integral equations, Quasilinear parabolic equations, and Feynman–Kac formula26 cited
    • 2022Path dependent Feynman–Kac formula for forward backward stochastic Volterra integral equations24 cited
    • 2016Pseudo-Markovian viscosity solutions of fully nonlinear degenerate PPDEs21 cited
    • 2017Functional Itô calculus, path-dependence and the computation of Greeks19 cited
    • 2020Comparison of Viscosity Solutions of Semilinear Path-Dependent PDEs19 cited
    • 2018Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle18 cited
    • 2020Viscosity Solutions of Path-Dependent PDEs with Randomized Time18 cited