
Multilevel Monte Carlo estimation of expected information gains
In this paper we develop an efficient Monte Carlo algorithm for estimati...
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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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Optimal Nested Simulation Experiment Design via Likelihood Ratio Method
Nested simulation arises frequently in financial or input uncertainty qu...
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Efficient Debiased Variational Bayes by Multilevel Monte Carlo Methods
Variational Bayes is a method to find a good approximation of the poster...
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Adaptive Multilevel Monte Carlo for Probabilities
We consider the numerical approximation of ℙ[G∈Ω] where the ddimensiona...
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On the Opportunities and Pitfalls of Nesting Monte Carlo Estimators
We present a formalization of nested Monte Carlo (NMC) estimation, where...
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Optimal Learning from the DoobDynkin lemma
The DoobDynkin Lemma gives conditions on two functions X and Y that ens...
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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 from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may resort to nested simulation. To reduce the complexity of nested simulation, we present a method that combines multilevel Monte Carlo (MLMC) and quasiMonte Carlo (QMC). In the outer simulation, we use Monte Carlo to generate financial scenarios. In the inner simulation, we use QMC to estimate the portfolio loss in each scenario. We prove that using QMC can accelerate the convergence rates in both the crude nested simulation and the multilevel nested simulation. Under certain conditions, the complexity of MLMC can be reduced to O(ϵ^2(logϵ)^2) by incorporating QMC. On the other hand, we find that MLMC encounters catastrophic coupling problem due to the existence of indicator functions. To remedy this, we propose a smoothed MLMC method which uses logistic sigmoid functions to approximate indicator functions. Numerical results show that the optimal complexity O(ϵ^2) is almost attained when using QMC methods in both MLMC and smoothed MLMC, even in moderate high dimensions.
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