MLMC for nested expectations
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 difficul...
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| Format: | Book section |
| Language: | English |
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Springer
2018
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| Summary: | 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 (1) smooth, (2) continuous and piecewise smooth, or (3) discontinuous. |
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