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Applicable Analysis
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Volume 100, 2021 - Issue 16
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Articles

Generalized mean-field backward stochastic differential equations and related partial differential equations

Pages 3299-3321 | Received 02 Feb 2019, Accepted 09 Jan 2020, Published online: 23 Jan 2020

References

  • Pardoux E, Peng S. Adapted solution of a backward stochastic differential equation. Syst Control Lett. 1990;14:55–61.
  • Chen Z, Epstein L. Ambiguity, risk, and asset returns in continuous time. Econometrica. 2002;70:1403–1443.
  • El Karoui N, Peng S, Quenez MC. Backward stochastic differential equations in finance. Math Finance. 1997;7:1–71.
  • Peng S. Backward stochastic differential equations and applications to optimal control. Appl Math Optim. 1993;27:125–144.
  • Hamadene S, Lepeltier JP. Zero-sum stochastic differential games and backward equations. Syst Control Lett. 1995;24:259–263.
  • Pardoux E. Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order. In: Stochastic analysis and related topics VI. Vol. 42. Boston (MA): Birkhäuser; 1998. p. 79–127.
  • Pardoux E, Peng S. Backward stochastic differential equations and quasilinear parabolic partial differential equations. In: Stochastic partial differential equations and their applications. Vol. 176. Berlin: Springer; 1992. p. 200–217.
  • Peng S. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stoch Stoch Rep. 1991;37:61–74.
  • Pardoux E, Zhang S. Generalized BSDEs and nonlinear Neumann boundary value problems. Probab Theory Relat Fields. 1998;110:535–558.
  • Lions PL, Sznitman AS. Stochastic differential equations with reflecting boundary conditions. Commun Pure Appl Math. 1984;37:511–537.
  • Saisho Y. Stochastic differential equations for multi-dimensional domain with reflecting boundary. Probab Theory Relat Fields. 1987;74:455–477.
  • Barles G, Buckdahn R, Pardoux E. Backward stochastic differential equations and integral-partial differential equations. Stochastics: Int J Probab Stoch Process. 1997;60:57–83.
  • Ma J, Cvitanić J. Reflected forward-backward SDEs and obstacle problems with boundary conditions. Int J Stoch Anal. 2001;14:113–138.
  • Buckdahn R, Djehiche B, Li J, et al. Mean-field backward stochastic differential equations: a limit approach. Ann Probab. 2009;37:1524–1565.
  • Buckdahn R, Li J, Peng S. Mean-field backward stochastic differential equations and related partial differential equations. Stoch Process Their Appl. 2009;119:3133–3154.
  • Li J, Tang S. Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain. ESAIM: COCV. 2015;21:1150–1177.
  • Barles G. Fully non-linear Neumann type boundary conditions for second-order elliptic and parabolic equations. J Differ Equ. 1993;106:90–106.
  • Crandall MG, Ishii H, Lions PL. User ′s guide to viscosity solutions of second order partial differential equations. Bull Am Math Soc. 1992;27:1–67.

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