Open Access
Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 12 | |
Number of page(s) | 42 | |
DOI | https://doi.org/10.1051/cocv/2023086 | |
Published online | 28 February 2024 |
- J. Qiu, Controlled ordinary differential equations with random path-dependent coefficients and stochastic path-dependent Hamilton-Jacobi equations. Stochastic Processes Appl. 154 (2022) 1-25. [CrossRef] [MathSciNet] [Google Scholar]
- R. Cont, D.-A. Fournie, et al., Functional Itô calculus and stochastic integral representation of martingales. Ann. Probab. 41 (2013) 109-133. [CrossRef] [MathSciNet] [Google Scholar]
- D. Leao, A. Ohashi, A.B. Simas, et al., A weak version of path-dependent functional Ito calculus. Ann. Probab. 46 (2018) 3399-3441. [CrossRef] [MathSciNet] [Google Scholar]
- M.G. Crandall, L.C. Evans and P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Arn,. Math. Soc. 282 (1984) 487-502. [CrossRef] [Google Scholar]
- M.G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Arn,. Math. Soc. 277 (1983) 1-42. [CrossRef] [Google Scholar]
- H. Ishii and P.-L. Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. J. Differ. Equ. 83 (1990) 26-78. [CrossRef] [Google Scholar]
- R. Jensen, P.-L. Lions and P.E. Souganidis, A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations. Proc. Am. Math. Soc. 102 (1988) 975-978. [CrossRef] [Google Scholar]
- P.-L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Part 2: viscosity solutions and uniqueness. Commun. Part. Differ. Equ. 8 (1983) 1229-1276. [CrossRef] [Google Scholar]
- M.G. Crandall and P.-L. Lions, Hamilton-Jacobi equations in infinite dimensions I. Uniqueness of viscosity solutions. J. Funct. Anal. 62 (1985) 379-396. [CrossRef] [MathSciNet] [Google Scholar]
- P.-L. Lions, Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: The case of bounded stochastic evolutions. J. Funct. Anal. (1988). [Google Scholar]
- N.Y. Lukoyanov, On viscosity solution of functional Hamilton-Jacobi type equations for hereditary systems. Proc. Steklov Inst. Math. 259 (2007) S190-S200. [CrossRef] [Google Scholar]
- I. Ekren, N. Touzi and J. Zhang, Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part I. Ann. Probab. 44 (2016) 1212-1253. [MathSciNet] [Google Scholar]
- I. Ekren and J. Zhang, Pseudo-Markovian viscosity solutions of fully nonlinear degenerate PPDEs. Probab. Uncertainty Quant. Risk 1 (2016) 1-34. [CrossRef] [MathSciNet] [Google Scholar]
- Z. Ren, N. Touzi and J. Zhang, Comparison of viscosity solutions of fully nonlinear degenerate parabolic path-dependent PDEs. SIAM J. Math. Anal. 49 (2017) 4093-4116. [CrossRef] [MathSciNet] [Google Scholar]
- A. Cosso, S. Federico, F. Gozzi, M. Rosestolato and N. Touzi, Path-dependent equations and viscosity solutions in infinite dimension. Ann. Probab. 46 (2018) 126-174. [CrossRef] [MathSciNet] [Google Scholar]
- S. Peng and F. Wang, BSDE, Path-dependent PDE and nonlinear Feynman-Kac formula. Sci. China Math. 59 (2016) 19-36. [CrossRef] [MathSciNet] [Google Scholar]
- H. Mete Soner, On the Hamilton-Jacobi-Bellman equations in Banach spaces. J. Optim. Theory Appl. 57 (1988) 429-437. [CrossRef] [MathSciNet] [Google Scholar]
- E. Bayraktar and C. Keller, Path-dependent Hamilton-Jacobi equations in infinite dimensions. J. Funct. Anal. 275 (2018) 2096-2161. [CrossRef] [MathSciNet] [Google Scholar]
- C. Bender and N. Dokuchaev, A first-order BSPDE for swing option pricing. Math. Finance 26 (2016) 461-491. [CrossRef] [MathSciNet] [Google Scholar]
- J. Qiu, Viscosity solutions of stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 56 (2018) 3708-3730. [CrossRef] [MathSciNet] [Google Scholar]
- J. Qiu and W. Wei, Uniqueness of viscosity solutions of stochastic Hamilton-Jacobi equations. Acta Math. Sci. 39 (2019) 857-873. [CrossRef] [MathSciNet] [Google Scholar]
- E. Bayraktar and J. Qiu, Controlled reflected SDEs and Neumann problem for backward SPDEs. Ann. Appl. Probab. 29 (2019) 2819-2848. [MathSciNet] [Google Scholar]
- P. Cardaliaguet, F. Delarue, J.-M. Lasry and P.-L. Lions, The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201). Princeton University Press (2019). [Google Scholar]
- Y. Hu, J. Ma and J. Yong, On semi-linear degenerate backward stochastic partial differential equations. Probab. Theory Related Fields 123 (2002) 381-411. [CrossRef] [MathSciNet] [Google Scholar]
- S. Peng, Stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 30 (1992) 284-304. [CrossRef] [MathSciNet] [Google Scholar]
- G. Fabbri, F. Gozzi and A. Swiech, Stochastic optimal control in infinite dimension. Probability and Stochastic Modelling. Springer (2017). [CrossRef] [Google Scholar]
- C. Prévôt and M. Rockner, A Concise Course on Stochastic Partial Differential Equations, Vol. 1905. Springer (2007). [Google Scholar]
- R. Buckdahn, C. Keller, J. Ma and J. Zhang, Fully nonlinear stochastic and rough PDEs: classical and viscosity solutions. Probab. Uncertainty Quant. Risk 5 (2020) 1-59. [CrossRef] [MathSciNet] [Google Scholar]
- I. Ekren, N. Touzi and J. Zhang, Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II. Ann. Probab. 44 (2016) 2507-2553. [MathSciNet] [Google Scholar]
- H. Kunita, Some extensions of Ito’s formula, in Seminaire de Probabilites XV 1979/80. Springer (1981) 118-141. [CrossRef] [Google Scholar]
- G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge University Press (2014). [CrossRef] [Google Scholar]
- B. Øksendal, Stochastic Differential Equations. Springer (2003). [CrossRef] [Google Scholar]
- P. Briand, B. Delyon, Y. Hu, E. Pardoux and L. Stoica, Lp solutions of backward stochastic differential equations. Stochastic Processes Appl. 108 (2003) 604-618. [Google Scholar]
- N.V. Krylov, Nonlinear Elliptic and Parabolic Equations of the Second Order, Vol. 7. Springer (1987). [CrossRef] [Google Scholar]
- J. Qiu, Weak solution for a class of fully nonlinear stochastic Hamilton-Jacobi-Bellman equations. Stochastic Processes Appl. 127 (2017) 1926-1959. [CrossRef] [MathSciNet] [Google Scholar]
- I. Karatzas, S.E. Shreve, I. Karatzas and S.E. Shreve, Methods of Mathematical FINANCE, Vol. 39. Springer (1998). [Google Scholar]
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