Type
Conference PaperKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Applied Mathematics and Computational Science Program
Stochastic Numerics Research Group
Date
2011-08-23Online Publication Date
2011-08-23Print Publication Date
2012Permanent link to this record
http://hdl.handle.net/10754/575782
Metadata
Show full item recordAbstract
This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael B. Giles. (Michael Giles. Oper. Res. 56(3):607–617, 2008.) for the approximation of expected values depending on the solution to an Itô stochastic differential equation. The work (Michael Giles. Oper. Res. 56(3):607– 617, 2008.) proposed and analyzed a forward Euler multilevelMonte Carlo method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a standard, single level, Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretizations, generated by an adaptive algorithmintroduced in (AnnaDzougoutov et al. Raùl Tempone. Adaptive Monte Carlo algorithms for stopped diffusion. In Multiscale methods in science and engineering, volume 44 of Lect. Notes Comput. Sci. Eng., pages 59–88. Springer, Berlin, 2005; Kyoung-Sook Moon et al. Stoch. Anal. Appl. 23(3):511–558, 2005; Kyoung-Sook Moon et al. An adaptive algorithm for ordinary, stochastic and partial differential equations. In Recent advances in adaptive computation, volume 383 of Contemp. Math., pages 325–343. Amer. Math. Soc., Providence, RI, 2005.). This form of the adaptive algorithm generates stochastic, path dependent, time steps and is based on a posteriori error expansions first developed in (Anders Szepessy et al. Comm. Pure Appl. Math. 54(10):1169– 1214, 2001). Our numerical results for a stopped diffusion problem, exhibit savings in the computational cost to achieve an accuracy of ϑ(TOL),from(TOL−3), from using a single level version of the adaptive algorithm to ϑ(((TOL−1)log(TOL))2).Citation
Hoel, H., von Schwerin, E., Szepessy, A., & Tempone, R. (2011). Adaptive Multilevel Monte Carlo Simulation. Lecture Notes in Computational Science and Engineering, 217–234. doi:10.1007/978-3-642-21943-6_10Publisher
Springer NatureConference/Event name
Proceedings of a Winter Workshop at the Banff International Research StationISBN
978-3-642-21942-9ae974a485f413a2113503eed53cd6c53
10.1007/978-3-642-21943-6_10