Approximation and error analysis of forward-backward SDEs driven by general Lévy processes using shot noise series representations
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Date
2021
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Abstract
We consider the simulation of a system of decoupled forward-backward stochastic differential
equations (FBSDEs) driven by a pure jump Lévy process L and an independent Brownian motion
B. We allow the Lévy process L to have an infinite jump activity. Therefore, it is necessary for the
simulation to employ a finite approximation of its Lévy measure. We use the generalized shot noise
series representation method by Rosinski (2001) to approximate the driving Lévy process L. We
compute the Lp error, p > 2, between the true and the approximated FBSDEs which arises from
the finite truncation of the shot noise series (given sufficient conditions for existence and uniqueness
of the FBSDE). We also derive the Lp error between the true solution and the discretization of the
approximated FBSDE using an appropriate backward Euler scheme.
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Keywords
decoupled forward-backward SDEs with jumps, Euler Scheme, Discrete-time approximation, shot noise series representation, Lévy processes