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Volumn 60, Issue 7, 2007, Pages 1081-1110

Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs

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EID: 34249723795     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20168     Document Type: Article
Times cited : (204)

References (52)
  • 1
    • 0000580597 scopus 로고
    • Backward-forward stochastic differential equations
    • Antonelli, F. Backward-forward stochastic differential equations. Ann. Appl. Probab. 3 (1993), no. 3, 777-793.
    • (1993) Ann. Appl. Probab , vol.3 , Issue.3 , pp. 777-793
    • Antonelli, F.1
  • 2
    • 0040606325 scopus 로고
    • Necessary optimally conditions in problems of the control of stochastic differential equations
    • Arkin, V. I.; Saksonov, M. T. Necessary optimally conditions in problems of the control of stochastic differential equations. Dokl. Akad. Nauk SSSR 244 (1979), no. 1, 11-15.
    • (1979) Dokl. Akad. Nauk SSSR , vol.244 , Issue.1 , pp. 11-15
    • Arkin, V.I.1    Saksonov, M.T.2
  • 3
    • 0037843726 scopus 로고    scopus 로고
    • Error analysis of the optimal quantization algorithm for obstacle problems
    • Bally, V.; Pagès, G. Error analysis of the optimal quantization algorithm for obstacle problems. Stochastic Process. Appl. 106 (2003), no. 1, 1-40.
    • (2003) Stochastic Process. Appl , vol.106 , Issue.1 , pp. 1-40
    • Bally, V.1    Pagès, G.2
  • 4
    • 0142168487 scopus 로고    scopus 로고
    • Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods
    • Barles, G.; Biton, S.; Bourgoing, M.; Ley, O. Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods. Calc. Var. Partial Differential Equations 18 (2003), no. 2, 159-179.
    • (2003) Calc. Var. Partial Differential Equations , vol.18 , Issue.2 , pp. 159-179
    • Barles, G.1    Biton, S.2    Bourgoing, M.3    Ley, O.4
  • 5
    • 0002508109 scopus 로고    scopus 로고
    • Backward stochastic differential equations and integral-partial differential equations
    • Barles, G.; Buckdahn, R.; Pardoux, E. Backward stochastic differential equations and integral-partial differential equations. Stochastics Stochastics Rep. 60 (1997), no. 1-2, 57-83.
    • (1997) Stochastics Stochastics Rep , vol.60 , Issue.1-2 , pp. 57-83
    • Barles, G.1    Buckdahn, R.2    Pardoux, E.3
  • 6
    • 0024070155 scopus 로고
    • Exit time problems in optimal control and vanishing viscosity method
    • Barles, G.; Perthame, B. Exit time problems in optimal control and vanishing viscosity method. SIAM J. Control Optim. 26 (1988), no. 5, 1133-1148.
    • (1988) SIAM J. Control Optim , vol.26 , Issue.5 , pp. 1133-1148
    • Barles, G.1    Perthame, B.2
  • 7
    • 0000929070 scopus 로고
    • Conjugate convex functions in optimal stochastic control
    • Bismut, J.-M. Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl. 44 (1973), 384-404.
    • (1973) J. Math. Anal. Appl , vol.44 , pp. 384-404
    • Bismut, J.-M.1
  • 8
    • 0007791583 scopus 로고
    • Contrôle des systèmes linéaires quadratiques: Applications de l'intégrale stochastique
    • Séminaire de Probabilités, XII Univ. Strasbourg, Strasbourg, 1976/1977, Springer, Berlin
    • Bismut, J.-M. Contrôle des systèmes linéaires quadratiques: applications de l'intégrale stochastique. Séminaire de Probabilités, XII (Univ. Strasbourg, Strasbourg, 1976/1977), 180-264. Lecture Notes in Mathematics, 649. Springer, Berlin, 1978.
    • (1978) Lecture Notes in Mathematics , vol.649 , pp. 180-264
    • Bismut, J.-M.1
  • 9
    • 2342427092 scopus 로고    scopus 로고
    • Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
    • Bouchard, B.; Touzi, N. Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations. Stochastic Process. Appl. 111 (2004), no. 2, 175-206.
    • (2004) Stochastic Process. Appl , vol.111 , Issue.2 , pp. 175-206
    • Bouchard, B.1    Touzi, N.2
  • 11
    • 0030516708 scopus 로고    scopus 로고
    • Valuation of the early-exercise price for options using simulations and nonparametric regression
    • Carriere, J. F. Valuation of the early-exercise price for options using simulations and nonparametric regression. Insurance Math. Econom. 19 (1996), no. 1, 19-30.
    • (1996) Insurance Math. Econom , vol.19 , Issue.1 , pp. 19-30
    • Carriere, J.F.1
  • 12
    • 32144449613 scopus 로고    scopus 로고
    • Equivalent and absolutely continuous measure changes for jump-diffusion processes
    • Cheridito, P.; Filipović, D.; Yor, M. Equivalent and absolutely continuous measure changes for jump-diffusion processes. Ann. Appl. Probab. 15 (2005), no. 3, 1713-1732.
    • (2005) Ann. Appl. Probab , vol.15 , Issue.3 , pp. 1713-1732
    • Cheridito, P.1    Filipović, D.2    Yor, M.3
  • 13
    • 30844453791 scopus 로고    scopus 로고
    • Small time path behavior of double stochastic integrals and applications to stochastic control
    • Cheridito, P.; Soner, H. M.; Touzi, N. Small time path behavior of double stochastic integrals and applications to stochastic control. Ann. Appl. Probab. 15 (2005), no. 4, 2472-2495.
    • (2005) Ann. Appl. Probab , vol.15 , Issue.4 , pp. 2472-2495
    • Cheridito, P.1    Soner, H.M.2    Touzi, N.3
  • 14
    • 24944463132 scopus 로고    scopus 로고
    • The multi-dimensional super-replication problem under gamma constraints
    • Cheridito, P.; Soner, H. M.; Touzi, N. The multi-dimensional super-replication problem under gamma constraints. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 5, 633-666.
    • (2005) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.22 , Issue.5 , pp. 633-666
    • Cheridito, P.1    Soner, H.M.2    Touzi, N.3
  • 15
    • 0038394778 scopus 로고    scopus 로고
    • Numerical methods for backward stochastic differential equations
    • Publications of the Newton Institute. Cambridge University Press, Cambridge
    • Chevance, D. Numerical methods for backward stochastic differential equations. Numerical methods in finance, 232-244. Publications of the Newton Institute. Cambridge University Press, Cambridge, 1997.
    • (1997) Numerical methods in finance , pp. 232-244
    • Chevance, D.1
  • 16
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • Crandall, M. G.; Ishii, H.; Lions, P.-L. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 1, 1-67.
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 17
    • 0030360242 scopus 로고    scopus 로고
    • Backward stochastic differential equations with reflection and Dynkin games
    • Cvitanić, J.; Karatzas, I. Backward stochastic differential equations with reflection and Dynkin games. Ann. Probab. 24 (1996), no. 4, 2024-2056.
    • (1996) Ann. Probab , vol.24 , Issue.4 , pp. 2024-2056
    • Cvitanić, J.1    Karatzas, I.2
  • 18
    • 0032237817 scopus 로고    scopus 로고
    • Backward stochastic differential equations with constraints on the gains-process
    • Cvitanić, J.; Karatzas, I.; Soner, H. M. Backward stochastic differential equations with constraints on the gains-process. Ann. Probab. 26 (1998), no. 4, 1522-1551.
    • (1998) Ann. Probab , vol.26 , Issue.4 , pp. 1522-1551
    • Cvitanić, J.1    Karatzas, I.2    Soner, H.M.3
  • 19
    • 0030510296 scopus 로고    scopus 로고
    • Hedging options for a large investor and forward-backward SDE's
    • Cvitanić, J.; Ma, J. Hedging options for a large investor and forward-backward SDE's. Ann. Appl. Probab. 6 (1996), no. 2, 370-398.
    • (1996) Ann. Appl. Probab , vol.6 , Issue.2 , pp. 370-398
    • Cvitanić, J.1    Ma, J.2
  • 20
    • 0036233502 scopus 로고    scopus 로고
    • On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case
    • Delarue, F. On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case. Stochastic Process. Appl. 99 (2002), no. 2, 209-286.
    • (2002) Stochastic Process. Appl , vol.99 , Issue.2 , pp. 209-286
    • Delarue, F.1
  • 21
    • 33645699121 scopus 로고    scopus 로고
    • A forward-backward stochastic algorithm for quasi-linear PDEs
    • Delarue, P.; Menozzi, S. A forward-backward stochastic algorithm for quasi-linear PDEs. Ann. Appl. Probab. 16 (2006), no. 1, 140-184.
    • (2006) Ann. Appl. Probab , vol.16 , Issue.1 , pp. 140-184
    • Delarue, P.1    Menozzi, S.2
  • 22
    • 0030520557 scopus 로고    scopus 로고
    • Numerical methods for forward-backward stochastic differential equations
    • Douglas, J., Jr.; Ma, J.; Protter, P. Numerical methods for forward-backward stochastic differential equations. Ann. Appl. Probab. 6 (1996), no. 3, 940-968.
    • (1996) Ann. Appl. Probab , vol.6 , Issue.3 , pp. 940-968
    • Douglas Jr., J.1    Ma, J.2    Protter, P.3
  • 23
    • 0031542653 scopus 로고    scopus 로고
    • Backward stochastic differential equations in finance
    • El Karoui, N.; Peng, S.; Quenez, M. C. Backward stochastic differential equations in finance. Math. Finance 7 (1997), no. 1, 1-71.
    • (1997) Math. Finance , vol.7 , Issue.1 , pp. 1-71
    • El Karoui, N.1    Peng, S.2    Quenez, M.C.3
  • 24
    • 0003228130 scopus 로고    scopus 로고
    • Partial differential equations
    • American Mathematical Society, Providence, R.I
    • Evans, L. C. Partial differential equations. Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, R.I., 1998.
    • (1998) Graduate Studies in Mathematics , vol.19
    • Evans, L.C.1
  • 25
    • 0003294328 scopus 로고
    • Controlled Markov processes and viscosity solutions
    • Springer, New York
    • Fleming, W. H.; Soner, H. M. Controlled Markov processes and viscosity solutions. Applications of Mathematics, 25. Springer, New York, 1993.
    • (1993) Applications of Mathematics , vol.25
    • Fleming, W.H.1    Soner, H.M.2
  • 26
    • 1542342296 scopus 로고    scopus 로고
    • Applications of Mathematics, 53. Stochastic Modelling and Applied Probability. Springer, New York
    • Glasserman, P. Monte Carlo methods in financial engineering. Applications of Mathematics, 53. Stochastic Modelling and Applied Probability. Springer, New York, 2004.
    • (2004) Monte Carlo methods in financial engineering
    • Glasserman, P.1
  • 27
    • 29144464083 scopus 로고    scopus 로고
    • A regression-based Monte Carlo method to solve backward stochastic differential equations
    • Gobet, E.; Lemor, J.-P.; Warin, X. A regression-based Monte Carlo method to solve backward stochastic differential equations. Ann. Appl. Probab. 15 (2005), no. 3, 2172-2202.
    • (2005) Ann. Appl. Probab , vol.15 , Issue.3 , pp. 2172-2202
    • Gobet, E.1    Lemor, J.-P.2    Warin, X.3
  • 28
    • 34249677083 scopus 로고    scopus 로고
    • Ikeda, N.; Watanabe, S. Stochastic differential equations and diffusion processes. 2nd ed. North-Holland Mathematical Library, 24. North-Holland, Amsterdam; Kodansha, Tokyo, 1989.
    • Ikeda, N.; Watanabe, S. Stochastic differential equations and diffusion processes. 2nd ed. North-Holland Mathematical Library, 24. North-Holland, Amsterdam; Kodansha, Tokyo, 1989.
  • 29
    • 0000102848 scopus 로고
    • Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations
    • Ishii, H. Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations. Indiana Univ. Math. J. 33 (1984), no. 5, 721-748.
    • (1984) Indiana Univ. Math. J , vol.33 , Issue.5 , pp. 721-748
    • Ishii, H.1
  • 30
    • 0003242243 scopus 로고
    • Brownian motion and stochastic calculus
    • 2nd ed, Springer, New York
    • Karatzas, I.; Shreve, S. E. Brownian motion and stochastic calculus. 2nd ed. Graduate Texts in Mathematics, 113. Springer, New York, 1991.
    • (1991) Graduate Texts in Mathematics , vol.113
    • Karatzas, I.1    Shreve, S.E.2
  • 34
    • 34249736125 scopus 로고    scopus 로고
    • Liptser, R. S.; Shiryaev, A. N. Statistics of random processes. I. General theory. Applications of Mathematics, 5. Stochastic Modelling and Applied Probability. Springer, Berlin, 2001.
    • Liptser, R. S.; Shiryaev, A. N. Statistics of random processes. I. General theory. Applications of Mathematics, 5. Stochastic Modelling and Applied Probability. Springer, Berlin, 2001.
  • 35
    • 0035578679 scopus 로고    scopus 로고
    • Valuing American options by simulation: A simple least-squares approach
    • Longstaff, F. A.; Schwartz, E. S. Valuing American options by simulation: a simple least-squares approach. Rev. Fin. Stud. 14 (2001), no. 1, 113-147.
    • (2001) Rev. Fin. Stud , vol.14 , Issue.1 , pp. 113-147
    • Longstaff, F.A.1    Schwartz, E.S.2
  • 36
    • 0036101915 scopus 로고    scopus 로고
    • Numerical method for backward stochastic differential equations
    • Ma, J.; Protter, P.; San Martín, J.; Torres, S. Numerical method for backward stochastic differential equations. Ann. Appl. Probab. 12 (2002), no. 1, 302-316.
    • (2002) Ann. Appl. Probab , vol.12 , Issue.1 , pp. 302-316
    • Ma, J.1    Protter, P.2    San Martín, J.3    Torres, S.4
  • 37
    • 0344891803 scopus 로고
    • Solving forward-backward stochastic differential equations explicitly - a four step scheme
    • Ma, J.; Protter, P.; Yong, J. M. Solving forward-backward stochastic differential equations explicitly - a four step scheme. Probab. Theory Related Fields 98 (1994), no. 3, 339-359.
    • (1994) Probab. Theory Related Fields , vol.98 , Issue.3 , pp. 339-359
    • Ma, J.1    Protter, P.2    Yong, J.M.3
  • 38
    • 84877611045 scopus 로고    scopus 로고
    • Forward-backward stochastic differential equations and their applications
    • Springer, Berlin
    • Ma, J.; Yong, J. Forward-backward stochastic differential equations and their applications. Lecture Notes in Mathematics, 1702. Springer, Berlin, 1999.
    • (1999) Lecture Notes in Mathematics , vol.1702
    • Ma, J.1    Yong, J.2
  • 39
    • 0025262967 scopus 로고
    • Adapted solution of a backward stochastic differential equation
    • Pardoux, É.; Peng, S. G. Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 (1990), no. 1, 55-61.
    • (1990) Systems Control Lett , vol.14 , Issue.1 , pp. 55-61
    • Pardoux, E.1    Peng, S.G.2
  • 40
    • 0000268709 scopus 로고
    • Backward stochastic differential equations and quasilinear parabolic partial differential equations
    • Stochastic partial differential equations and their applications Charlotte, NC, Springer, Berlin
    • Pardoux, É.; Peng, S. G. Backward stochastic differential equations and quasilinear parabolic partial differential equations. Stochastic partial differential equations and their applications (Charlotte, NC, 1991), 200-217. Lecture Notes in Control and Information Sciences, 176. Springer, Berlin, 1992.
    • (1991) Lecture Notes in Control and Information Sciences , vol.176 , pp. 200-217
    • Pardoux, E.1    Peng, S.G.2
  • 41
    • 21344492007 scopus 로고
    • Backward doubly stochastic differential equations and systems of quasilinear SPDEs
    • Pardoux, É.; Peng, S. G. Backward doubly stochastic differential equations and systems of quasilinear SPDEs. Probab. Theory Related Fields 98 (1994), no. 2, 209-227.
    • (1994) Probab. Theory Related Fields , vol.98 , Issue.2 , pp. 209-227
    • Pardoux, E.1    Peng, S.G.2
  • 42
    • 0033463544 scopus 로고    scopus 로고
    • Forward-backward stochastic differential equations and quasilinear parabolic PDEs
    • Pardoux, E.; Tang, S. Forward-backward stochastic differential equations and quasilinear parabolic PDEs. Probab. Theory Related Fields 114 (1999), no. 2, 123-150.
    • (1999) Probab. Theory Related Fields , vol.114 , Issue.2 , pp. 123-150
    • Pardoux, E.1    Tang, S.2
  • 43
    • 0025462369 scopus 로고
    • A general stochastic maximum principle for optimal control problems
    • Peng, S. G. A general stochastic maximum principle for optimal control problems. SIAM J. Control Optim. 28 (1990), no. 4, 966-979.
    • (1990) SIAM J. Control Optim , vol.28 , Issue.4 , pp. 966-979
    • Peng, S.G.1
  • 44
  • 45
    • 0002686129 scopus 로고
    • Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
    • Peng, S. G. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stochastics Stochastics Rep. 37 (1991), no. 1-2, 61-74.
    • (1991) Stochastics Stochastics Rep , vol.37 , Issue.1-2 , pp. 61-74
    • Peng, S.G.1
  • 46
    • 0001098095 scopus 로고
    • A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation
    • Peng, S. G. A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation. Stochastics Stochastics Rep. 38 (1992), no. 2, 119-134.
    • (1992) Stochastics Stochastics Rep , vol.38 , Issue.2 , pp. 119-134
    • Peng, S.G.1
  • 47
    • 0026834859 scopus 로고
    • Stochastic Hamilton-Jacobi-Bellman equations
    • Peng, S. G. Stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 30 (1992), no. 2, 284-304.
    • (1992) SIAM J. Control Optim , vol.30 , Issue.2 , pp. 284-304
    • Peng, S.G.1
  • 48
    • 0003318214 scopus 로고
    • Backward stochastic differential equations and applications to optimal control
    • Peng, S. G. Backward stochastic differential equations and applications to optimal control. Appl. Math. Optim. 27 (1993), no. 2, 125-144.
    • (1993) Appl. Math. Optim , vol.27 , Issue.2 , pp. 125-144
    • Peng, S.G.1
  • 49
    • 0037249034 scopus 로고    scopus 로고
    • Stochastic target problems, dynamic programming, and viscosity solutions
    • Soner, H. M.; Touzi, N. Stochastic target problems, dynamic programming, and viscosity solutions. SIAM J. Control Optim. 41 (2002), no. 2, 404-424.
    • (2002) SIAM J. Control Optim , vol.41 , Issue.2 , pp. 404-424
    • Soner, H.M.1    Touzi, N.2
  • 50
    • 34249711614 scopus 로고    scopus 로고
    • Stroock, D. W.; Varadhan, S. R. S. On the support of diffusion processes with applications to the strong maximum principle. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), III: Probability theory, 333-359. University of California Press, Berkeley, Calif., 1972.
    • Stroock, D. W.; Varadhan, S. R. S. On the support of diffusion processes with applications to the strong maximum principle. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, 333-359. University of California Press, Berkeley, Calif., 1972.
  • 51
    • 0008220051 scopus 로고    scopus 로고
    • Probabilistic numerical methods for partial differential equations: Elements of analysis
    • Probabilistic models for nonlinear partial differential equations Montecatini Terme, 1995, Springer, Berlin
    • Talay, D. Probabilistic numerical methods for partial differential equations: elements of analysis. Probabilistic models for nonlinear partial differential equations (Montecatini Terme, 1995), 148-196. Lecture Notes in Mathematics, 1627. Springer, Berlin, 1996.
    • (1996) Lecture Notes in Mathematics , vol.1627 , pp. 148-196
    • Talay, D.1


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