We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method.
- Authors
Fujii, Masaaki; Takahashi, Akihiko
- Abstract
In this paper, we propose an efficient Monte Carlo implementation of a non-linear FBSDE as a system of interacting particles inspired by the idea of the branching diffusion method of McKean. It will be particularly useful to investigate large and complex systems, and hence it is a good complement of our previous work presenting an analytical perturbation procedure for generic non-linear FBSDEs. There appear multiple species of particles, where the first one follows the diffusion of the original underlying state, and the others the Malliavin derivatives with a grading structure. The number of branching points are capped by the order of perturbation, which is expected to make the scheme less numerically intensive. The proposed method can be applied to semi-linear problems, such as American options, credit and funding value adjustments, and even fully non-linear issues, such as the optimal portfolio problems in incomplete and/or constrained markets.
- Subjects
STOCHASTIC differential equations; ASYMPTOTIC expansions; PERTURBATION theory; PARTICLE methods (Numerical analysis); NONLINEAR equations
- Publication
Asia-Pacific Financial Markets, 2015, Vol 22, Issue 3, p283
- ISSN
1387-2834
- Publication type
Article
- DOI
10.1007/s10690-015-9201-7