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SUMMARY:Multilevel Nested Simulation for Efficient Risk Estimation - Abdul
  Lateef Haji Ali (University of Oxford)
DTSTART:20180306T144500Z
DTEND:20180306T153000Z
UID:TALK101887@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We investigate the problem of computing a nested expectation o
 f the form P[E[X|Y] >= 0] = E[H(E[X|Y])] where H is the Heaviside function
 . This nested expectation appears\, for example\, when estimating the prob
 ability of a large loss from a financial portfolio.  We present a method t
 hat combines the idea of using Multilevel Monte Carlo (MLMC) for nested ex
 pectations with the idea of adaptively selecting the number of samples in 
 the approximation of the inner expectation\, as proposed by (Broadie et al
 .\, 2011). We propose and analyse an algorithm that adaptively selects the
  number of inner samples on each MLMC level and prove that the resulting M
 LMC method with adaptive sampling has an order e^-2|log(e)|^2 complexity t
 o achieve a root mean-squared error e.  The theoretical analysis is verifi
 ed by numerical experiments on a simple model problem.  Joint work with: M
 ichael B. Giles (University of Oxford)
LOCATION:Seminar Room 1\, Newton Institute
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