2011/10/23 by Soufiane Aazizi, Aazizi, Soufiane · 4 citations
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Applied mathematics #Brownian motion #Convergence (economics) #Discretization #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Jump #Jump process #Lévy process #Mathematical analysis #Mathematics #Physics #Stochastic differential equation #Stochastic processes and financial applications #math.PR #msc:60H07 #msc:60H35 #msc:60J75
paper · pdf · doi:10.48550/arxiv.1110.5059
published in arXiv (Cornell University) (Cornell University)
arxiv created 2011/10/23 · openalex publication_date 2011/10/23 · arxiv updated 2011/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new algorithms to discretize a decoupled forward backward stochastic differential equations driven by pure jump Lévy process (FBSDEL in short). The method is built in two steps. Firstly, we approximate the FBSDEL by a forward backward stochastic differential equations driven by a Brownian motion and Poisson process (FBSDEBP in short), in which we replace the small jumps by a Brownian motion. Then, we prove the convergence of the approximation when the size of small jumps \eps goes to 0. In the second step, we obtain the Lp Hölder continuity of the solution of FBSDEBP and we construct two numerical schemes for this FBSDEBP. Based on the Lp Hölder estimate, we prove the convergence of the scheme when the number of time steps n goes to infinity. Combining these two steps leads to prove the convergence of numerical schemes to the solution of FBSDEL.