Local Control Regression: Improving the Least Squares Monte Carlo Method for Portfolio Optimization

TL;DR

This paper introduces a local control regression method with adaptive grids to enhance the efficiency and accuracy of the least squares Monte Carlo algorithm in portfolio optimization.

Contribution

It proposes a novel local control regression approach with adaptive grids, improving computational efficiency and accuracy over classical global methods.

Findings

Local regression with adaptive grids yields accurate results with coarser grids.

The method reduces computational costs compared to classical global control regression.

Enhanced portfolio optimization performance demonstrated through experiments.

Abstract

The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to generalize the discrete estimates. However, the classical global control regression can be expensive and inaccurate. To overcome this difficulty, we introduce a local control regression technique, combined with adaptive grids. We show that choosing a coarse grid for local regression can produce sufficiently accurate results.