Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations*,**
School of Mathematics and System Science, Shandong University,
250100 Jinan, P.R. China. email@example.com.
2 Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, CAS (No. 2008DP173182), P.R. China. firstname.lastname@example.org.
3 Department of Financial Mathematics and Control science, School of Mathematical Science, Fudan University, 200433 Shanghai, P.R. China.
Revised: 26 November 2009
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.
Mathematics Subject Classification: 60H10 / 34K28
Key words: Backward stochastic differential equations / reflected stochastic differential equations with one barrier / numerical algorithm / numerical simulation
© EDP Sciences, SMAI, 2010