A decomposition approach for the discrete-time approximation of BSDEs with a jump II: the quadratic case

2012/11/27 by Idris Kharroubi, Kharroubi, Idris, Thomas Lim +1 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Control Systems Optimization #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR

paper · pdf · doi:10.48550/arxiv.1211.6231

arxiv created 2012/11/27 · openalex publication_date 2012/11/27 · arxiv updated 2012/11/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Discrete-time approximation of decoupled Forward–Backward SDE with jumps

Cited by

• A decomposition approach for the discrete-time approximation of FBSDEs with a jump

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