Adaptive weak approximation of reflected and stopped diffusions

Christian Bayer, Anders Szepessy, Raul Tempone

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We study the weak approximation problem of diffusions, which are reflected at a subset of the boundary of a domain and stopped at the remaining boundary. First, we derive an error representation for the projected Euler method of Costantini, Pacchiarotti and Sartoretto [Costantini et al., SIAM J. Appl. Math., 58(1):73-102, 1998], based on which we introduce two new algorithms. The first one uses a correction term from the representation in order to obtain a higher order of convergence, but the computation of the correction term is, in general, not feasible in dimensions d > 1. The second algorithm is adaptive in the sense of Moon, Szepessy, Tempone and Zouraris [Moon et al., Stoch. Anal. Appl., 23:511-558, 2005], using stochastic refinement of the time grid based on a computable error expansion derived from the representation. Regarding the stopped diffusion, it is based in the adaptive algorithm for purely stopped diffusions presented in Dzougoutov, Moon, von Schwerin, Szepessy and Tempone [Dzougoutov et al., Lect. Notes Comput. Sci. Eng., 44, 59-88, 2005]. We give numerical examples underlining the theoretical results. © de Gruyter 2010.
Original languageEnglish (US)
Pages (from-to)1-67
Number of pages67
JournalMonte Carlo Methods and Applications
Volume16
Issue number1
DOIs
StatePublished - Jan 2010

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Adaptive weak approximation of reflected and stopped diffusions'. Together they form a unique fingerprint.

Cite this