Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations

By Bruno Bouchard, Nizar Touzi. 2004

610 citations recorded by the source corpus.

Subfields: Demography, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/fb04bed2c2af888f2b5f37371ffde293b12ab8d1

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Citations in the corpus

Numerical simulation of quadratic BSDEs (2013, neutral): “The classical (squared) error estimate for the discrete-time approximation of Lipschitz BSDEs is C n with n the number of time steps, but the constant C depends strongly on the Lipschitz constant of f̃M with respect to z and so it depends on M ; see, for example, [5, 43].”
On some recent aspects of stochastic control and their applications (2005, methodology): “We mention for BSDE the Markov chain approximation in [64], regression methods in [43], quantization methods in [4], the Monte-Carlo Malliavin method in [ 18 ] , and for FBSDE the four-step scheme in [29], and quantization method in [28].”
Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations (2006, methodology): “Squared error for different algorithms with respect to the complexity C with basis HC and P = 1 (see Gobet and Lemor 2006 for details) Section 2 Gobet and Lemor (2006) Bouchard and Touzi (2004)”
Discrete time approximation of decoupled Forward-Backward SDE with jumps (2008, methodology): “In the no-jump case, i.e. β = 0, the numerical approximation of (1.1) has already been studied in the literature; see e.g. Zhang [24], Bally and Pages [2], Bouchard and Touzi [7] or Gobet et al. [16].”
Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition (2011, neutral): “Let us precise the classical result shown by [3, 29, 22].”
Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition (2011, methodology): “Besides the fact that this variation gives a strong insight into the quantitative behavior of the BSDE, in particular var2(ξ, f, τ) was used to describe the error in adapted backward Euler schemes for ξ = g(XT ) with g being a Lipschitz function; see [5, 23] for implicit schemes and [15, 16] for exp”
Second order discretization of backward SDEs and simulation with the cubature method (2014, methodology): “Assuming that all coefficients of (1) are at least Lipschitz continuous in their spatial variables, we have, following [5] and [26], that”
Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations (2017, neutral): “…and Schwab (2004) for deterministic approximation methods for PDEs, to Bally and Pagès (2003), Bender and Denk (2007), Bender et al. (2017), Bouchard and Touzi (2004), Chassagneux (2014), Chassagneux and Crisan (2014), Chassagneux and Richou (2015, 2016), Crisan and Manolarakis (2010,…”
Time discretization and Markovian iteration for coupled FBSDEs (2008, methodology): “The stochastic control approach in Cvitani¢ and Zhang (2005) faces the same kind of di culty.”
OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS (2008, methodology): “The asymptotic properties of the resulting numerical algorithm for the computation of the price of American put options (and more generally, for the expected value of functions of the solutions of reflected backward stochastic differential equations) have been analyzed by Bouchard and Touzi [4].”
RUNGE-KUTTA SCHEMES FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS (2014, methodology): “These schemes are based on the well-known Runge–Kutta methods for ODEs and include new high order schemes as well as existing low order schemes such as the classical extension of the Euler scheme to BSDEs; see, for example, [1, 2, 4, 6].”
Pricing Asset Scheduling Flexibility using Optimal Switching (2008, methodology): “More generally, it has been proven (Bouchard and Touzi, 2004, Theorem 4.1) that if one directly approximates Et1 with an independent Monte Carlo simulation, then the resulting rate of convergence in the Lp-norm is O Dt{1{d=4p:N{2p .”