`Regression Anytime' with Brute-Force SVD Truncation

TL;DR

This paper introduces a new least-squares Monte Carlo method utilizing brute-force SVD truncation to efficiently approximate conditional expectations, with applications in option pricing and PDE discretization.

Contribution

It presents a novel regression algorithm that combines SVD truncation with variance reduction, improving convergence rates for stochastic dynamic programming problems.

Findings

Achieves arbitrarily fast polynomial convergence under smoothness assumptions

Applicable to Euler approximations of stochastic differential equations

Enhances dynamic programming solutions in finance and PDEs

Abstract

We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, e.g., in non-linear option pricing problems or in probabilistic discretization schemes for fully non-linear parabolic partial differential equations. Our algorithm can be generically applied when the underlying dynamics stem from an Euler approximation to a stochastic differential equation. A built-in variance reduction ensures that the convergence in the number of samples to the true regression function takes place at an arbitrarily fast polynomial rate, if the problem under consideration is smooth enough.