Mathematics
Probability
Scientist
Statistical Romberg extrapolation: A new variance reduction method and applications to option pricing
Theorems Limit With Weight For The Vectorial Martingales To Continuous Time
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Ahmed Kebaier has received 1 rating(s) and 1 review(s), resulting in an average rating of 4.20 on a scale from 1 to 5. The overall rating for this scientist is very good.
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Kebaier (2005) is a seminal paper in what became known after Giles (2006) as the Multilevel Monte Carlo method. In spite of this Kebaier (2005) has gone largely unnoticed by the community. Giles (2006), who cites Kebaier (2005), wrote a very clear and concise paper that became the primary reference (170 cites and more to date) in the field. I was familiar with Giles, but having just read Kebaier's paper and I found it very deep and insightful: it contains the cornerstone idea of reducing variance, and thus computational complexity of the algorithm, by combining 2 different levels of discretization (in a Romberg-style). Kebaier shows thus that instead of n^3, the cost can be reduced to n^(7/3). Giles improved and simplified this result, by taking an arbitrary number of levels L instead of 2 and thus managing to reduce the complexity to n^2 log(n)^p where p=p(L). Note that although Giles result is better than Kebaier's, the bulk of the improvement in the exponent is due to Kebaier's idea.
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