| Issue |
ESAIM: M2AN
Volume 45, Number 2, March-April 2011
|
|
|---|---|---|
| Page(s) | 335 - 360 | |
| DOI | https://doi.org/10.1051/m2an/2010059 | |
| Published online | 24 August 2010 | |
Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations*,**
1
School of Mathematics and System Science, Shandong University,
250100 Jinan, P.R. China. This email address is being protected from spambots. You need JavaScript enabled to view it.
.
2
Key Laboratory of Random Complex Structures and Data
Science, Academy of Mathematics and Systems Science, CAS (No. 2008DP173182), P.R. China. This email address is being protected from spambots. You need JavaScript enabled to view it.
.
3
Department of Financial Mathematics and Control science,
School of Mathematical Science, Fudan University, 200433 Shanghai, P.R. China.
Received:
13
November
2008
Revised:
26
November
2009
Abstract
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
This work is partly supported by the National Basic Research Program of China (973 Program), No. 2007CB814902 and No. 2007CB814906.
Second author is also partly supported by Youth Grant of National Science Foundation (No. 10901154/A0110) and financial support of president fund of AMSS, CAS.
© EDP Sciences, SMAI, 2010
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