  We introduce a simulation method for dynamic portfolio valuation and risk
management building on machine learning with kernels. We learn the dynamic
value process of a portfolio from a finite sample of its cumulative cash flow.
The learned value process is given in closed form thanks to a suitable choice
of the kernel. We show asymptotic consistency and derive finite sample error
bounds under conditions that are suitable for finance applications. Numerical
experiments show good results in large dimensions for a moderate training
sample size.
