
Multilevel Monte Carlo estimation of the expected value of sample information
We study Monte Carlo estimation of the expected value of sample informat...
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Efficient risk estimation via nested multilevel quasiMonte Carlo simulation
We consider the problem of estimating the probability of a large loss fr...
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Scalable computation for Bayesian hierarchical models
The article is about algorithms for learning Bayesian hierarchical model...
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Subsampling and other considerations for efficient risk estimation in large portfolios
Computing risk measures of a financial portfolio comprising thousands of...
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Tensor Processing Units for Financial Monte Carlo
Monte Carlo methods are core to many routines in quantitative finance su...
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Accelerating System Adequacy Assessment using the Multilevel Monte Carlo Approach
Accurately and efficiently estimating system performance under uncertain...
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Multilevel Monte Carlo Acceleration of Seismic Wave Propagation under Uncertainty
We interpret uncertainty in the parameters of a model for seismic wave p...
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Adaptive Multilevel Monte Carlo for Probabilities
We consider the numerical approximation of ℙ[G∈Ω] where the ddimensional random variable G cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations {G_ℓ}_ℓ∈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 suboptimal computational complexities since estimation of the probability involves a discontinuous functional of G_ℓ. We propose a general adaptive framework which is able to return the MLMC complexities seen for smooth or Lipschitz functionals of G_ℓ. 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 = 𝔼[XY] is approximated by an inner Monte Carlo estimate. Further experiments are given for digital option pricing, involving an approximation of a ddimensional SDE.
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