# Machine learning with kernels for portfolio valuation and risk management

## TL;DR

This paper presents a kernel-based machine learning method for dynamic portfolio valuation and risk management, providing a closed-form solution with proven consistency and practical effectiveness in high-dimensional settings.

## Contribution

It introduces a novel simulation approach that learns the portfolio value process from data using kernels, with theoretical guarantees and efficient numerical implementation.

## Key findings

- Demonstrates asymptotic consistency of the method
- Provides finite sample error bounds applicable to finance
- Shows good numerical performance in high-dimensional scenarios

## Abstract

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.