2024/09/16 by Acharya, Atithi, Yalovetzky, Romina, Minssen, Pierre +10 · 5 citations
#Data Analysis #FOS: Economics and business #FOS: Mathematics #FOS: Physical sciences #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Quantum Physics (quant-ph) #Risk Management (q-fin.RM) #Statistics and Probability (physics.data-an)
paper · doi:10.48550/arxiv.2409.10301
Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline targeting portfolio optimization and rebalancing problems with constraints. The pipeline decomposes the optimization problem into constrained subproblems, which are then solved separately and aggregated to give a final result. Our pipeline includes three main components: preprocessing of correlation matrices based on random matrix theory, modified spectral clustering based on Newman's algorithm, and risk rebalancing. Our empirical results show that our pipeline consistently decomposes real-world portfolio optimization problems into subproblems with a size reduction of approximately 80%. Since subproblems are then solved independently, our pipeline drastically reduces the total computation time for state-of-the-art solvers. Moreover, by decomposing large problems into several smaller subproblems, the pipeline enables the use of near-term quantum devices as solvers, providing a path toward practical utility of quantum computers in portfolio optimization.