Hybrid Approaches to Portfolio Optimization: Deep Neural Networks and Statistical Methods

Financial portfolio optimization presents a complex challenge at the intersection of mathematics, statistics, and finance. This study aims to determine the optimal combination of asset weights in a portfolio by considering various mathematical formulations, business constraints, and the dynamic nature of financial markets. We propose a novel approach that utilizes a solution bank to guide the search for the best investment strategy. Our methodology features individual portfolio solver agents that contribute optimal solutions to the solution bank, which are then utilized by a super-agent solver to make informed investment decisions. This framework incorporates diverse problem formulations and employs both deterministic solvers and evolutionary swarm-intelligence techniques to optimize portfolio weights using a Deep Neural Network model. What's more, we enhance the Simulated Annealing algorithm with a neighborhood generation mechanism that integrates heuristic knowledge and controlled perturbation strategies from financial literature. Empirical validation of our approach fixed under various market scenarios, including bearish and inflation-affected conditions.