Adaptive Multi Level Monte Carlo Simulation
2012 (English)In: Lecture Notes in Computational Science and Engineering, Vol. 82, 217-234 p.Article in journal (Refereed) Published
This work generalizes a multilevel Forward Euler Monte Carlo methodintroduced in  for the approximation of expected values depending onthe solution to an Itˆo stochastic differential equation. The work  proposedand analyzed a Forward Euler Multilevel Monte Carlo method basedon a hierarchy of uniform time discretizations and control variates to reducethe computational effort required by a standard, single level, ForwardEuler Monte Carlo method. This work introduces an adaptive hierarchyof non uniform time discretizations, generated by adaptive algorithms introducedin [11, 10]. These adaptive algorithms apply either deterministictime steps or stochastic time steps and are based on a posteriori error expansionsfirst developed in . Under sufficient regularity conditions, ournumerical results, which include one case with singular drift and one withstopped diffusion, exhibit savings in the computational cost to achieve anaccuracy of O(TOL), from O`TOL−3´to O“`TOL−1 log (TOL)´2”. Wealso include an analysis of a simplified version of the adaptive algorithmfor which we prove similar accuracy and computational cost results.
Place, publisher, year, edition, pages
Springer, 2012. Vol. 82, 217-234 p.
computational finance, Monte Carlo, multi-level, adaptivity, weak approximation, error control, Euler–Maruyama method, a posteriori error estimates, backward dual functions, adjoints
Engineering and Technology
IdentifiersURN: urn:nbn:se:kth:diva-12918DOI: 10.1007/978-3-642-21943-6_10OAI: oai:DiVA.org:kth-12918DiVA: diva2:319597
FunderSwedish e‐Science Research Center
QC 201201242010-05-182010-05-182014-01-29Bibliographically approved