MLMC for Nested Expectations

Michael B. Giles ()
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Michael B. Giles: University of Oxford, Mathematical Institute

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 425-442 from Springer

Abstract: Abstract This paper discusses progress and future research possibilities in applying MLMC ideas to nested expectations of the form 𝔼 [ g ( 𝔼 [ f ( X , Y ) | X ] ) ] $${\mathbb {E}}[\, g({\mathbb {E}}[\,f(X,Y) | X]) \,]$$ , 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-72456-0_20

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DOI: 10.1007/978-3-319-72456-0_20

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