A Constrained Consensus Based Optimization algorithm and its Application to Finance

TL;DR

This paper introduces a new constrained consensus-based optimization algorithm tailored for convex feasible sets, demonstrating its effectiveness in solving portfolio optimization problems in finance through simulation results.

Contribution

The paper extends the CBO algorithm to handle constrained non-convex optimization problems on convex domains, with practical application to financial portfolio optimization.

Findings

Successfully finds optimal asset weights in portfolio optimization

Demonstrates effectiveness through simulation results

Generalizes existing CBO algorithms to constrained settings

Abstract

In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the global minima of the non-convex function defined on a convex domain. As a practical application of the proposed algorithm, we study the portfolio optimization problem in finance. In this application, we introduce an objective function to choose the optimal weight on each asset in a asset-bundle which yields the maximal expected returns given a certain level of risks. Simulation results show that our proposed predictor-corrector type model is successful in finding the optimal value.