  We present an algorithm (CoDeFi) which overcomes the curse of dimensionality
(CoD) in scientific computations and, especially, in mathematical finance (Fi).
Our method applies a broad class of partial differential equations such as
Kolmogorov-type equations and, for instance, the Black and Scholes equation. As
a main feature, our algorithm allows one to solve partial differential
equations in large dimensions and provides a general framework for stochastic
problems. In insurance or finance applications, the number of dimensions
corresponds to the number of risk sources and it is crucial to have a numerical
method that remains robust and reliable in large dimensions.
