  For three applications of central interest in finance, we demonstrate the
relevance of numerical algorithms based on reproducing kernel Hilbert space
(RKHS) techniques. Three use cases are investigated. First, we show that
extrapolating from few pricer examples leads to sufficiently accurate and
computationally efficient results so that our algorithm can serve as a pricing
framework. The second use case concerns reverse stress testing, which is
formulated as an inversion function problem and is treated here via an optimal
transport technique in combination with the notions of kernel-based encoders,
decoders, and generators. Third, we show that standard techniques for time
series analysis can be enhanced by using the proposed generative algorithms.
Namely, we use our algorithm in order to extend the validity of any given
quantitative model. Our approach allows for conditional analysis as well as for
escaping the `Gaussian world'. This latter property is illustrated here with a
portfolio investment strategy.
