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    MLMC for Nested Expectations

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    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])], 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 i) smooth, ii) continuous and piecewise smooth, or iii) discontinuous.</p
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