Discretisation of FBSDEs driven by càdlàg martingales. (English) Zbl 1333.60155
Summary: We study the discretisation of forward-backward stochastic differential equations (FBSDEs) driven by càdlàg martingales. We prove that under certain conditions imposed on the parameters of the FBSDE the time-discrete scheme we consider converges to the time-continuous equation in the \(L^2\)-sense. Moreover, we show that the \(L^2\)-norm of the error is of the order of the time step.
MSC:
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G44 | Martingales with continuous parameter |
| 60J75 | Jump processes (MSC2010) |
| 60G48 | Generalizations of martingales |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
Keywords:
forward-backward stochastic differetial equations; discretisation; càdlàg martingales; jump processes; semimartingales; Galtchouck-Kunita-Watanabe decompositionReferences:
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