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Path-dependent equations and viscosity solutions in infinite dimension
16 references·1 citing·34 second hop
Path-dependent equations and viscosity solutions in infinite dimension (2018)Path-dependent equations and viscosity so…Functional Itô calculus (2019)Functional Itô calculusStochastic Optimal Control in Infinite Dimension (2017)Stochastic Optimal Control in…Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part I (2016)Viscosity solutions of fully …Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations (2015)Path-dependent optimal stocha…On viscosity solutions of path dependent PDEs (2014)On viscosity solutions of pat…Functional Itô calculus and stochastic integral representation of martingales (2013)Functional Itô calculus and s…Stochastic Equations with Delay: Optimal Control via BSDEs and Regular Solutions of Hamilton–Jacobi–Bellman Equations (2010)Stochastic Equations with Del…Stochastic Differential Equations in Infinite Dimensions (2010)Stochastic Differential Equat…Change of variable formulas for non-anticipative functionals on path space (2010)Change of variable formulas f…A stochastic control problem with delay arising in a pension fund model (2010)A stochastic control problem …A functional extension of the Ito formula (2009)A functional extension of the…Backward stochastic differential equations and quasilinear parabolic partial differential equations (2005)Backward stochastic different…Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control (2002)Nonlinear Kolmogorov equation…Hamilton–Jacobi–Bellman Equations for the Optimal Control of the Duncan–Mortensen–Zakai Equation (2000)Hamilton–Jacobi–Bellman Equat…Integration and Probability (1995)Integration and ProbabilityViscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai's equation (1989)Viscosity solutions of fully …Path-dependent Hamilton–Jacobi equations in infinite dimensions (2018)Path-dependent Hamilton–Jacob…Brownian Motion and Stochastic Calculus (1988)Adapted solution of a backward stochastic differential equation (1990)Solving forward-backward stochastic differential equations explicitly — a four step scheme (1994)Backward stochastic differential equations and partial differential equations with quadratic growth (2000)Brownian Motion and Stochastic Calculus (2007)Differential equations driven by rough signals (1998)Continuous Martingales and Brownian Motion (1999)Stochastic Integration and Differential Equations (2005)Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2016)Backward Stochastic Differential Equations in Finance (1997)Controlled Markov Processes and Viscosity Solutions (2005)Backward stochastic differential equations driven by G -Brownian motion (2013)Dynamic programming approach to principal–agent problems (2017)Stochastic Analysis (1997)Limit Theorems for Stochastic Processes (2003)BSDE, path-dependent PDE and nonlinear Feynman-Kac formula (2015)A martingale approach for fractional Brownian motions and related path dependent PDEs (2019)The Malliavin Calculus and Related Topics (2006)BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces (2007)Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011)The stochastic maximum principle for optimal control problems of delay systems involving continuous and impulse controls (2012)The Pricing of Options and Corporate Liabilities (1973)Theory of Rational Option Pricing (1973)Theory of rational option pricing (2005)Reflected solutions of backward SDE's, and related obstacle problems for PDE's (1997)Feynman–Kac representation for Hamilton–Jacobi–Bellman IPDE (2015)Stochastic control for a class of nonlinear kernels and applications (2015)Systemic Risk and Stochastic Games with Delay (2018)Zero-sum stochastic differential games of generalized McKean–Vlasov type (2018)Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty (2021)The covariation for Banach space valued processes and applications (2013)Martingale representation theorems for initially enlarged filtrations (2000)A Fourier transform method for nonparametric estimation of multivariate volatility (2009)A fourier transform method for nonparametric estimation of multivariate volatility (2012)
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References

  • 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations782 cited
  • 2019Functional Itô calculus257 cited
  • 2013Functional Itô calculus and stochastic integral representation of martingales252 cited
  • 1995Integration and Probability203 cited
  • 2014On viscosity solutions of path dependent PDEs181 cited
  • 2010Change of variable formulas for non-anticipative functionals on path space172 cited
  • 2017Stochastic Optimal Control in Infinite Dimension169 cited
  • 2002Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control167 cited
  • 2010Stochastic Differential Equations in Infinite Dimensions166 cited
  • 2016Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part I119 cited
  • 2010A stochastic control problem with delay arising in a pension fund model89 cited
  • 2009A functional extension of the Ito formula72 cited
  • 1989Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai's equation67 cited
  • 2010Stochastic Equations with Delay: Optimal Control via BSDEs and Regular Solutions of Hamilton–Jacobi–Bellman Equations55 cited

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  • 2015Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations44 cited
  • 2000Hamilton–Jacobi–Bellman Equations for the Optimal Control of the Duncan–Mortensen–Zakai Equation44 cited
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    • 2018Path-dependent Hamilton–Jacobi equations in infinite dimensions32 cited