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2 results

17 - Gaussian Measures, Cylinder Measures, and Fields on B
from Part IV - Game Theoretic Approach on Banach Spaces
Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
Book:

Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization

Published online:

10 October 2019

Print publication:

24 October 2019, pp 347-359
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Summary

This chapter extends the presentation ofGaussian measures, cylinder measures, and fields fromSobolev spaces to Banach spaceswith quadratic energynorm. The relationship between weak distributions and cylinder measures is elucidated as is the relationship between Gaussian cylinder measures and Gaussian fields.

Pathwise large deviations for the rough Bergomi model
Part of
Antoine Jacquier, Mikko S. Pakkanen, Henry Stone
Journal:

Journal of Applied Probability / Volume 55 / Issue 4 / December 2018

Published online by Cambridge University Press:

16 January 2019, pp. 1078-1092

Print publication:

December 2018
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Introduced recently in mathematical finance by Bayer et al. (2016), the rough Bergomi model has proved particularly efficient to calibrate option markets. We investigate some of its probabilistic properties, in particular proving a pathwise large deviations principle for a small-noise version of the model. The exponential function (continuous but superlinear) as well as the drift appearing in the volatility process fall beyond the scope of existing results, and a dedicated analysis is needed.

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2 results

17 - Gaussian Measures, Cylinder Measures, and Fields on B

Summary

Pathwise large deviations for the rough Bergomi model