scholarly journals Large deviations for small noise diffusions in a fast markovian environment

2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Amarjit Budhiraja ◽  
Paul Dupuis ◽  
Arnab Ganguly
Keyword(s):  
Large Deviations ◽  
Small Noise ◽  
Markovian Environment

scholarly journals Large deviations and stochastic stability in the small noise double limit

2016 ◽  
Vol 11 (1) ◽  
pp. 279-355 ◽  
Author(s):  
William H. Sandholm ◽  
Mathias Staudigl
Keyword(s):  
Large Deviations ◽  
Stochastic Stability ◽  
Small Noise ◽  
Double Limit

scholarly journals Pathwise large deviations for the rough Bergomi model

2018 ◽  
Vol 55 (4) ◽  
pp. 1078-1092 ◽  
Author(s):  
Antoine Jacquier ◽  
Mikko S. Pakkanen ◽  
Henry Stone
Keyword(s):  
Large Deviations ◽  
Exponential Function ◽  
Mathematical Finance ◽  
Large Deviations Principle ◽  
Small Noise ◽  
Option Markets

Abstract 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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