Adaptive Optimal Allocation in Stratified Sampling Methods
By Pierre Etoré, Benjamin Jourdain. 2007
64 citations recorded by the source corpus.
In this paper, we propose a stratified sampling algorithm in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of further drawings in each stratum. These proportions converge to the optimal allocation in terms of variance reduction and our stratified estimator is asymptotically normal with asymptotic variance equal to the minimal one. Numerical experiments confirm the efficiency of our algorithm. For the pricing of arithmetic average Asian options in the Black and Scholes model, the variance is divided by a factor going from 1.1 to 50.4 (depending on the option type and the moneyness) in comparison with the standard allocation procedure, while the increase in computation time does not overcome 1%.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/d189819f40a193be453314f63b1aaa2639c1bb9c
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Citations in the corpus
- An Approximation of the Universal Intelligence Measure (2011, methodology): “There are various algorithms for adaptive stratified sampling, however we have chosen the method developed by Étoré and Jourdain (2010) as they have derived the confidence intervals for the estimate of the mean, a feature we will use when reporting our results.”