Time discretization and Markovian iteration for coupled FBSDEs

By Christian Bender, Jianfeng Zhang. 2008

135 citations recorded by the source corpus.

In this paper we lay the foundation for a numerical algorithm to simulate high-dimensional coupled FBSDEs under weak coupling or monotonicity conditions. In particular, we prove convergence of a time discretization and a Markovian iteration. The iteration differs from standard Picard iterations for FBSDEs in that the dimension of the underlying Markovian process does not increase with the number of iterations. This feature seems to be indispensable for an efficient iterative scheme from a numerical point of view. We finally suggest a fully explicit numerical algorithm and present some numerical examples with up to 10-dimensional state space.

Subfields: Control and Systems Engineering, Finance, Management Information Systems

View Paper: https://www.semanticscholar.org/paper/f14e106d938aad606a2fb9d8aacc5cbaafbd719e

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In Control and Systems Engineering

In Finance

In Management Information Systems

Citations in the corpus

TRUE UPPER BOUNDS FOR BERMUDAN PRODUCTS VIA NON‐NESTED MONTE CARLO (2009, background): “Due to the Lipschitz continuity of u(Tj+1, ·) results on L2-regularity obtained for the control part of FBSDEs in more general situations by Zhang (2004) and Bender and Zhang (2006) can be applied.”
Least-Squares Monte Carlo for Backward SDEs (2012, methodology): “Concerning the time discretization error, the convergence of this implicit scheme is also of order 1/2, see Bouchard and Touzi (2004). It requires, however, some iteration procedure to become explicit in time.”
Numerical method for FBSDEs of McKean–Vlasov type (2017, methodology): “In the classical case, this question has been addressed by several authors, among which [21, 22] and [7], but all these methods rely on the Markov structure of the problem.”
Error Criteria for Numerical Solutions of Backward SDEs (2010, methodology): “These convergence results for the time discretization were recently generalized to coupled systems of forward-backward SDEs by Bender and Zhang [8] and to non-Lipschitz terminal conditions by Gobet and Makhlouf [19].”
Second order discretization of backward SDEs and simulation with the cubature method (2014, methodology): “111 (2004) 175–206] and Zhang [Ann.”