2015/03/07 by Idris Kharroubi, Kharroubi, Idris, Thomas Lim +1
Economics, Econometrics and Finance · Mathematics · Social Sciences · #60G57 #60J75 #65C99 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60G57 #msc:60J75 #msc:65C99
paper · pdf · doi:10.48550/arxiv.1503.02152
31 pages. arXiv admin note: substantial text overlap with arXiv:1103.3029, arXiv:1211.6231
arxiv created 2015/03/07 · openalex publication_date 2015/03/07 · arxiv updated 2015/03/10 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We are concerned with the discretization of a solution of a Forward-Backward stochastic differential equation (FBSDE) with a jump process depending on the Brownian motion. In this paper, we study the cases of Lipschitz generators and the generators with a quadratic growth w.r.t. the variable z. We propose a recursive scheme based on a general existence result given in a companion paper and we study the error induced by the time discretization. We prove the convergence of the scheme when the number of time steps n goes to infinity. Our approach allows to get a convergence rate similar to that of schemes of Brownian FBSDEs.