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- W3183452362 abstract "We consider the numerical approximation of $mathbb{P}[Gin Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations ${G_ell}_{ellinmathbb{N}}$ which can be sampled. The cost of standard Monte Carlo estimation scales poorly with accuracy in this setup since it compounds the approximation and sampling cost. A direct application of Multilevel Monte Carlo improves this cost scaling slightly, but returns sub-optimal computational complexities since estimation of the probability involves a discontinuous functional of $G_ell$. We propose a general adaptive framework which is able to return the MLMC complexities seen for smooth or Lipschitz functionals of $G_ell$. Our assumptions and numerical analysis are kept general allowing the methods to be used for a wide class of problems. We present numerical experiments on nested simulation for risk estimation, where $G = mathbb{E}[X|Y]$ is approximated by an inner Monte Carlo estimate. Further experiments are given for digital option pricing, involving an approximation of a $d$-dimensional SDE." @default.
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- W3183452362 date "2021-07-19" @default.
- W3183452362 modified "2023-09-27" @default.
- W3183452362 title "Adaptive Multilevel Monte Carlo for Probabilities." @default.
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