[1]
|
Bally, V:Approximation scheme for solutions of BSDE, Backward stochastic differential equations, (Paris, 1995-1996), Pitman Res. Notes Math. Ser., vol. 364, pp. 177-191. Longman, Harlow (1997)
|
[2]
|
Bouchard, B, Touzi, N:Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations. Stoch. Process. Appl 111, 175-206 (2004)
|
[3]
|
Briand, P, Delyon, B, Mémin, J:Donsker-type theorem for BSDEs. Electron. Comm. Probab 6, 1-14(2001)
|
[4]
|
Chevance, D:Numerical methods for backward stochastic differential equations, Numerical methods in finance, Publ. Newton Inst., pp. 232-244. Cambridge Univ. Press, Cambridge (1997)
|
[5]
|
Crisan, D:Numerical methods for solving the stochastic filtering problem, Numerical methods and stochastics (Toronto, ON, 1999), Fields Inst. Commun., 34, Amer. Math. Soc., pp. 1-20, Providence, RI (2002)
|
[6]
|
Crisan, D, Lyons, T:Nonlinear filtering and measure-valued processes. Probab. Theory Related Fields 109, 217-244 (1997)
|
[7]
|
Crisan, D, Xiong, J:Numerical solution for a class of SPDEs over bounded domains. Stochastics 86(3), 450-472 (2014)
|
[8]
|
Cvitanić, J, Ma, J:Hedging options for a large investor and forward-backward SDE's. Ann. Appl. Probab 6, 370-398 (1996)
|
[9]
|
Cvitanić, J, Zhang, J:The steepest descent method for forward-backward SDEs. Electron. J. Probab 10, 1468-1495 (2005)
|
[10]
|
Del Moral, P:Non-linear filtering:interacting particle resolution. Markov Process. Related Fields 2 4, 555-581 (1996)
|
[11]
|
Delarue, F, Menozzi, S:A forward-backward stochastic algorithm for quasi-linear PDEs. Ann. Appl.Probab 16, 140-184 (2006)
|
[12]
|
Douglas, J Jr., Ma, J, Protter, P:Numerical methods for forward-backward stochastic differential equations. Ann. Appl. Probab 6, 940-968 (1996)
|
[13]
|
El Karoui, N, Peng, S, Quenez, MC:Backward stochastic differential equations in finance. Math. Finance 7, 1-71 (1997)
|
[14]
|
Föllmer, H, Schied, A:Convex measures of risk and trading constraints. Finance Stoch. 6 (2002), 429-447(1999). Springer-Verlag, New York Friedman, A:Stochastic Differential Equations and Applications. Vol. 1., Probability and Mathematical Statistics, vol. 28. Academic Press, New York-London (1975)
|
[15]
|
Henry-Labordère, P, Tan, X, Touzi, N:A numerical algorithm for a class of BSDEs via the branching process. Stochastic Process. Appl 124(2), 1112-1140 (2014)
|
[16]
|
Kurtz, T, Xiong, J:Particle representations for a class of nonlinear SPDEs. Stochastic Process. Appl 83, 103-126 (1999)
|
[17]
|
Kurtz, T, Xiong, J:Numerical solutions for a class of SPDEs with application to filtering, Stochastics in finite and infinite dimensions:in honor of Gopinath Kallianpur. Trends Math., pp. 233-258. Birkhuser Boston, Boston, MA (2001)
|
[18]
|
Liu, H, Xiong, J:A branching particle system approximation for nonlinear stochastic filtering. Sci. China Math 56, 1521-1541 (2013)
|
[19]
|
Ma, J, Protter, P, San Martin, J, Torres, S:Numerical method for backward stochastic differential equations. Ann. Appl. Probab 12, 302-316 (2002)
|
[20]
|
Ma, J, Protter, P, Yong, J:Solving forward-backward stochastic differential equations explicitly-a four step scheme. Probab. Theory Related Fields 98 3, 339-359 (1994)
|
[21]
|
Ma, J, Shen, J, Zhao, Y:On numerical approximations of forward-backward stochastic differential equations. SIAM J. Numer. Anal 46, 2636-2661 (2008)
|
[22]
|
Ma, J, Yong, J:Forward-backward stochastic differential equations and their applications. Springer-Verlag, Berlin (1999)
|
[23]
|
Ma, J, Zhang, J:Representations and regularities for solutions to BSDEs with reflections. Stochast.Process. Appl 115, 539-569 (2005)
|
[24]
|
Milstein, GN, Tretyakov, MV:Numerical algorithms for forward-backward stochastic differential equations. SIAM J. Sci. Comput 28, 561-582 (2006)
|
[25]
|
Pardoux, E, Peng, S:Adapted solution of a backward stochastic differential equation. Syst. Control Lett 14, 55-61 (1990)
|
[26]
|
Peng, S:Backward stochastic differential equation, nonlinear expectation and their applications. Proceedings of the International Congress of Mathematicians. Volume I, pp. 393-432. Hindustan Book Agency, New Delhi (2010)
|
[27]
|
Rosazza Gianin, E:Risk measures via g-expectations. Insurance Math. Econom 39, 19-34 (2006)
|
[28]
|
Xiong, J:An Introduction to Stochastic Filtering Theory. Oxford Graduate Texts in Mathematics, 18.Oxford University Press, Oxford (2008)
|
[29]
|
Xiong, J, Zhou, X:Mean-variance portfolio selection under partial information. SIAM J. Control Optim 46, 156-175 (2007)
|
[30]
|
Yong, J, Zhou, X:Stochastic Controls. Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999)
|
[31]
|
Zhang, J:A numerical scheme for BSDEs. Ann. Appl. Probab 14, 459-488 (2004)
|