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Note on Viscosity Solution of Path-Dependent PDE and G-Martingales
16 references·2 citing·29 second hop
Note on Viscosity Solution of Path-Dependent PDE and G-Martingales (2011)Note on Viscosity Solution of Path-Depend…Nonlinear Expectations and Stochastic Calculus under Uncertainty (2019)Nonlinear Expectations and St…BSDE, path-dependent PDE and nonlinear Feynman-Kac formula (2015)BSDE, path-dependent PDE and …On viscosity solutions of path dependent PDEs (2014)On viscosity solutions of pat…Random $G$-expectations (2013)Random $G$-expectationsSome properties on G-evaluation and its applications to G-martingale decomposition (2011)Some properties on G-evaluati…Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011)Backward Stochastic Different…Martingale representation theorem for the G -expectation (2010)Martingale representation the…Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations (2009)Survey on normal distribution…G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type (2007)G-Expectation, G-Brownian Mot…NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS (2005)NONLINEAR EXPECTATIONS AND NO…Controlled Markov Processes and Viscosity Solutions (2005)Controlled Markov Processes a…Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims (2004)Filtration Consistent Nonline…Stochastic controls : Hamiltonian systems and HJB equations (1999)Stochastic controls : Hamilto…Stochastic Hamilton–Jacobi–Bellman Equations (1992)Stochastic Hamilton–Jacobi–Be…A Generalized dynamic programming principle and hamilton-jacobi-bellman equation (1992)A Generalized dynamic program…Adapted solution of a backward stochastic differential equation (1990)Adapted solution of a backwar…Theory, methods and meaning of nonlinear expectation theory (2017)Theory, methods and meaning o…Stochastic differential equations driven by G -Brownian motion and ordinary differential equations (2014)Stochastic differential equat…The Pricing of Options and Corporate Liabilities (1973)Stochastic Differential Equations and Diffusion Processes (1983)Martingale Methods in Financial Modelling (1997)Brownian Motion and Stochastic Calculus (2007)Mean field games (2007)Controlled Diffusion Processes (1980)A General Stochastic Maximum Principle for Optimal Control Problems (1990)Filtration-consistent nonlinear expectations and related g-expectations (2002)Nonlinear Expectations, Nonlinear Evaluations and Risk Measures (2004)Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs (2006)Backward Stochastic Differential Equations in Finance (1997)Backward stochastic differential equations driven by G -Brownian motion (2013)Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2016)Dynamic programming approach to principal–agent problems (2017)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)Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations (2019)Ambiguity, Risk, and Asset Returns in Continuous Time (2002)Stopping times and related Itô’s calculus with G -Brownian motion (2011)Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications (2015)Stochastic Differential Equations (2003)Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths (2010)Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework (2000)Backward stochastic differential equations and quasilinear parabolic partial differential equations (2005)Mean-Variance Portfolio Selection with Random Parameters in a Complete Market (2002)Quasi-sure Stochastic Analysis through Aggregation (2011)Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by G -Brownian motion (2013)
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References

  • 2005Controlled Markov Processes and Viscosity Solutions2,698 cited
  • 1990Adapted solution of a backward stochastic differential equation2,676 cited
  • 1999Stochastic controls : Hamiltonian systems and HJB equations1,780 cited
  • 2007G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type621 cited
  • 2019Nonlinear Expectations and Stochastic Calculus under Uncertainty594 cited
  • 1992Stochastic Hamilton–Jacobi–Bellman Equations307 cited
  • 1992A Generalized dynamic programming principle and hamilton-jacobi-bellman equation296 cited
  • 2009Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations220 cited
  • 2010Martingale representation theorem for the G -expectation201 cited
  • 2014On viscosity solutions of path dependent PDEs181 cited
  • 2011Some properties on G-evaluation and its applications to G-martingale decomposition163 cited
  • 2005NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS159 cited
  • 2004Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims133 cited
  • 2011Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications121 cited
  • 2015

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BSDE, path-dependent PDE and nonlinear Feynman-Kac formula
83 cited
  • 2013Random $G$-expectations71 cited
  • Cited by

    • 2017Theory, methods and meaning of nonlinear expectation theory40 cited
    • 2014Stochastic differential equations driven by G -Brownian motion and ordinary differential equations27 cited