On Optimizating Portfolio Returns via A Modified Dynamic Programming (DP) Model Based on Bellman's Equation: Identifying Finest Cluster Shape

Abstract

Effective financial management leads to the development of suitable decision plans that aim for optimal results when investing in a competitive stock portfolio. This research adapted and utilized a dynamic programming (DP) model developed by Bellman to address the financial issue. There are challenges in selecting an investment that produces maximum returns; the problem has led to economic crisis among investors in financial markets. Many financial analysts offer investors accurate and unverified investment details, leading to suboptimal or no returns and various investment issues. The objectives of this study are to maximize investor returns and to confirm the findings by employing two statistical validity tests to determine the most suitable test for this study. Two tests (Silhouette and Dunn) have been utilized for result validation. By utilizing Silhouette, the computation became simpler and produced a more reliable and superior result. The method of k-means clustering demonstrated superior statistical evaluation, optimal fit, and improved investment patterns. Compared with earlier studies, the introduction of a system variable in this study yielded the highest return in the initial stage. In the end, the purpose of verified investment reports was achieved, minimize mistakes frequently made by financial managers and stack holders during their investment plans and in choosing portfolios.