N° 19-34: Machine Learning With Kernels for Portfolio Valuation and Risk Management

We introduce a computational framework for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the replicating martingale of a portfolio from a finite sample of its terminal cumulative cash flow. The learned replicating martingale is given in closed form thanks to a suitable choice of the kernel. We develop an asymptotic theory and prove convergence and a central limit theorem. We also derive finite sample error bounds and concentration inequalities. Numerical examples show good results for a relatively small training sample size.