CBO algorithm with average drift and applications to portfolio optimization

TL;DR

This paper introduces a novel consensus-based optimization algorithm with average drift (Ad-CBO), demonstrating its theoretical convergence and superior performance in static, dynamic, and financial portfolio optimization tasks.

Contribution

The paper develops the Ad-CBO algorithm with a theoretical convergence framework and applies it effectively to portfolio optimization under stochastic market conditions.

Findings

Ad-CBO converges to a global minimizer.

Ad-CBO outperforms CBO in speed and accuracy.

Ad-CBO effectively optimizes portfolios in real-time.

Abstract

We propose a consensus based optimization algorithm with average drift (in short Ad-CBO) and provide a theoretical framework for it. In the theoretical analysis, we show that particle solutions to Ad-CBO converge to a global minimizer. In numerical simulations, we examine Ad-CBO's performance in optimizing static and dynamic objective functions. As a real-time application, we test the efficiency of Ad-CBO to find the optimal portfolio given stochastically evolving multi-asset prices in a financial market. The proposed Ad-CBO exhibits higher searching speed, lower tracking errors and regret bound than the CBO without stochastic diffusion