312 research outputs found
A decomposition approach for the discrete-time approximation of BSDEs with a jump II: the quadratic case
We study the discrete-time approximation for solutions of quadratic forward
back- ward stochastic differential equations (FBSDEs) driven by a Brownian
motion and a jump process which could be dependent. Assuming that the generator
has a quadratic growth w.r.t. the variable z and the terminal condition is
bounded, we prove the convergence of the scheme when the number of time steps n
goes to infinity. Our approach is based on the companion paper [15] and allows
to get a convergence rate similar to that of schemes of Brownian FBSDEs
Time discretization and Markovian iteration for coupled FBSDEs
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.Comment: Published in at http://dx.doi.org/10.1214/07-AAP448 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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