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PRODID:-//Memento EPFL//
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SUMMARY:Adaptive multilevel Monte Carlo simulation of Ito SDEs
DTSTART:20120418T161500
DTEND:20120418T180000
DTSTAMP:20260502T073117Z
UID:5c232b8a8cd7b907831a665491ebfc96b8285e90f59cc4c2965ac355
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr Erik Von Schwerin\nWe consider the numerical approximation 
 of expected values of functionals of solutions to Ito Stochastic Different
 ial Equations (SDE). This problem has many applications in physics and fin
 ance\, such as pricing financial contracts in the Black-Scholes model. The
  multilevel Monte Carlo method (MLMC) was introduced in the context of for
 ward Euler time stepping for Ito SDEs by M. Giles in [1] based on a hierar
 chy of uniform time discretizations and control variates to significantly 
 reduce the computational effort required by a standard\, single level\, Fo
 rward Euler Monte Carlo method. This talk reviews our recent results on a 
 generalisation of MLMC to adaptive time stepping algorithms [2\,3]. The ad
 aptive MLMC method uses a hierarchy of non uniform time discretisations\, 
 generated by adaptive algorithms previously introduced in [4\, 5] and base
 d on a posteriori error expansions following [6]. Adaptive time stepping i
 s advantageous in cases where constant step size has decreased convergence
  rate due to lower regularity. Under sufficient regularity conditions\, bo
 th our analysis and numerical results\, which include one case with singul
 ar drift and one with stopped diffusion\, exhibit savings in the computati
 onal cost to achieve an accuracy of O(TOL)\, from O(TOL3) using the single
  level adaptive method to O(TOL1 log(TOL))2 using the multilevel adaptive 
 method \; for these test problems single level uniform Euler time stepping
  has a complexity O(TOL4).
LOCATION:MAA331
STATUS:CONFIRMED
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