]; for applications, see [EHM08] and [EPQ97]; for numerics, see This list is not exhaustive Stochastic simulation: Algorithms and analysis . Stochastic Modelling and Applied Probability 57, Complementary references: for theoretical aspects, 2007. ,
Computational Methods for Option Pricing. SIAM series, Frontiers in Applied Mathematics, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00111740
On irregular functionals of SDEs and the Euler scheme, Finance and Stochastics, vol.13, pp.381-401, 2009. ,
Théorie de la spéculation, Ann. Sci. École Norm. Sup, 1900. ,
A forward scheme for backward SDEs, Stochastic Processes and their Applications, pp.1793-1823, 2007. ,
DOI : 10.1016/j.spa.2007.03.005
Symmetrized Euler scheme for an efficient approximation of reflected diffusions, Journal of Applied Probability, vol.41, issue.3, pp.877-889, 2004. ,
Error analysis of the optimal quantization algorithm for obstacle problems, Stochastic Processes and their Applications, vol.106, issue.1, pp.1-40, 2003. ,
DOI : 10.1016/S0304-4149(03)00026-7
URL : https://hal.archives-ouvertes.fr/hal-00103987
Least-squares monte carlo for BSDEs, Numerical Methods in Finance. Series: Springer Proceedings in Mathematics, 2012. ,
The law of the Euler scheme for stochastic differential equations, Probability Theory and Related Fields, vol.8, issue.1, pp.104-143, 1996. ,
DOI : 10.1007/BF01303802
URL : https://hal.archives-ouvertes.fr/inria-00074427
Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, pp.175-206, 2004. ,
DOI : 10.1016/j.spa.2004.01.001
URL : https://hal.archives-ouvertes.fr/hal-00103046
Solving Backward Stochastic Differential Equations using the Cubature method, 2010. ,
Brownian motion and martingales in analysis, Wadsworth Mathematics Series. Wadsworth International Group, 1984. ,
Backward stochastic differential equations and applications, Indifference pricing: theory and applications, pp.267-320, 2008. ,
Reflected solutions of backward SDE's and related obstacle problems for PDE's ,
Backward Stochastic Differential Equations in Finance, Mathematical Finance, vol.7, issue.1, pp.1-71, 1997. ,
DOI : 10.1111/1467-9965.00022
Calcul d'Itô sans probabilités, Seminar on Probability, pp.143-150, 1979. ,
Functional integration and partial differential equations, Annals of Mathematics Studies, 1985. ,
Partial differential equations of parabolic type, 1964. ,
Stochastic differential equations and applications, 1975. ,
Stochastic differential equations and applications, 1976. ,
Generalized fractional smoothness and L p variation of BSDEs with non-Lipschitz terminal condition, Stochastic Processes and their Applications, pp.2078-2116, 2012. ,
A distribution-free theory of nonparametric regression, 2002. ,
DOI : 10.1007/b97848
Matrix computations, 1996. ,
Numerical simulation of BSDEs using empirical regression methods: theory and practice, Proceedings of the Fifth Colloquium on BSDEs, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00291199
Error expansion for the discretization of backward stochastic differential equations, Stochastic Processes and their Applications, pp.803-829, 2007. ,
DOI : 10.1016/j.spa.2006.10.007
URL : https://hal.archives-ouvertes.fr/hal-00019463
Solving BSDE with Adaptive Control Variate, SIAM Journal on Numerical Analysis, vol.48, issue.1, pp.257-277, 2010. ,
DOI : 10.1137/090755060
URL : https://hal.archives-ouvertes.fr/hal-00373350
Monte Carlo methods in Financial Engineering, 2003. ,
A regression-based Monte Carlo method to solve backward stochastic differential equations, The Annals of Applied Probability, vol.15, issue.3, pp.2172-2202, 2005. ,
DOI : 10.1214/105051605000000412
Sequential control variates for functionals of Markov processes, SIAM Journal on Numerical Analysis, vol.43, issue.3, pp.1256-1275, 2005. ,
Sequential Monte Carlo domain decomposition for the Poisson equation, Proceedings of the 17th IMACS World Congress, pp.11-15, 2005. ,
Sensitivity analysis using Itô-Malliavin calculus and martingales. Application to stochastic control problem, SIAM Journal of Control and Optimization, vol.43, issue.5, pp.1676-1713, 2005. ,
L 2 -time regularity of BSDEs with irregular terminal functions, Stochastic Processes and their Applications, pp.1105-1132, 2010. ,
Stopped diffusion processes: boundary corrections and overshoot, Stochastic Processes and Their Applications, pp.130-162, 2010. ,
Euler schemes for the weak approximation of killed diffusion, Stochastic Processes and their Applications, pp.167-197, 2000. ,
Euler schemes and half-space approximation for the simulation of diffusions in a domain Special Volume: Mathematical Modeling and Numerical Methods in Finance, chapter Advanced Monte Carlo methods for barrier and related exotic options, ESAIM: Probability and Statistics, pp.261-297, 2001. ,
Multi-step forward dynamic programming equation and empirical regression scheme for the (Y -Z) components of a BSDE, 2012. ,
On stochastic differential equations, Mem. Amer. Math. Soc, issue.4, 1951. ,
Robust adaptive importance sampling for normal random vectors, The Annals of Applied Probability, vol.19, issue.5, pp.1687-1718, 2009. ,
DOI : 10.1214/09-AAP595
URL : https://hal.archives-ouvertes.fr/hal-00334697
Probability essentials, 2003. ,
Backward stochastic differential equations and partial differential equations with quadratic growth. The Annals of Probability, pp.558-602, 2000. ,
Numerical solution of stochastic differential equations, 1995. ,
Brownian motion and stochastic calculus, 1991. ,
Stochastic differential equations and stochastic flows of diffeomorphisms . Ecole d'Eté de Probabilités de St-Flour XII, 1982 -Lecture Notes in Math, pp.144-305, 1984. ,
Sur certains processus stochastiques homogènes, Compositio Math, vol.7, pp.283-339, 1939. ,
Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations, Bernoulli, vol.12, issue.5, pp.889-916, 2006. ,
DOI : 10.3150/bj/1161614951
URL : https://hal.archives-ouvertes.fr/hal-00394976
Methodes de Monte Carlo pour les processus de transport et de diffusion, Collection Mathématiques et Applications, vol.29, 1998. ,
Forward-Backward Stochastic Differential Equations, Lecture Notes in Mathematics, vol.1702, 1999. ,
Dynamical theories of Brownian motion, N.J, 1967. ,
Variance reduction for simulated diffusions, SIAM Journal on Applied Mathematics, vol.54, issue.6, pp.1780-1805, 1994. ,
Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, Stochastic analysis and related topics, pp.79-127, 1996. ,
Adapted solution of a backward stochastic differential equation, Systems & Control Letters, vol.14, issue.1, pp.55-61, 1990. ,
DOI : 10.1016/0167-6911(90)90082-6
Backward stochastic differential equations and quasilinear parabolic partial differential equations, Stochastic partial differential equations and their applications, Proc. IFIP Int. Conf Domain decomposition methods in science and engineering, pp.200-217, 1991. ,
DOI : 10.1007/BFb0007334
Continuous martingales and Brownian motion. Grundlehren der Mathematischen Wissenschaften, 2005. ,
Monte Carlo methods in boundary value problems, Series in Computational Physics, 1991. ,
Proof that properly anticipated prices fluctuate randomly, Industrial Management Review, vol.6, pp.42-49, 1965. ,
Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Analysis and Applications, pp.8-494, 1990. ,
URL : https://hal.archives-ouvertes.fr/inria-00075490
A numerical scheme for BSDEs, Ann. Appl. Probab, vol.14, issue.1, pp.459-488, 2004. ,