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MLMC for Nested Expectations

  • Michael B. GilesEmail author
Chapter

Abstract

This paper discusses progress and future research possibilities in applying MLMC ideas to nested expectations of the form \({\mathbb {E}}[\, g({\mathbb {E}}[\,f(X,Y) | X]) \,]\), with an outer expectation with respect to one random variable X, and an inner conditional expectation with respect to a second random variable Y . The difficulty in treating such applications is shown to depend on whether the function g is (1) smooth, (2) continuous and piecewise smooth, or (3) discontinuous.

Notes

Acknowledgements

The author is very grateful to a number of people for discussions and collaborations: Ian Sloan and Frances Kuo on alternatives to the Multi-Index Monte Carlo method; Takashi Goda and Howard Thom on EVPPI estimation; Wenhui Gou, Abdul-Lateef Haji-Ali, Ralf Korn and Klaus Ritter on Value-at-Risk estimation.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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