An algebraic approach to Integer Portfolio problems
F. Castro, J. Gago, I. Hartillo, J. Puerto, J.M. Ucha (University, of Seville, Spain)
TL;DR
This paper introduces an algebraic method using Gr"obner bases to solve integer portfolio optimization problems, enabling more realistic modeling and efficient computation of optimal portfolios under risk constraints.
Contribution
It presents a novel algebraic approach leveraging Gr"obner bases for integer portfolio optimization, combining algebraic geometry with financial modeling.
Findings
Effective computation of test sets for portfolio problems
Enhanced optimization under risk constraints
Potential for more realistic portfolio models
Abstract
Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model. We propose an algebraic approach to maximize the expected return under a given admissible level of risk measured by the covariance matrix. To reach an optimal portfolio it is an essential ingredient the computation of different test sets (via Gr\"obner basis) of linear subproblems that are used in a dual search strategy.
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Taxonomy
TopicsRisk and Portfolio Optimization · Reservoir Engineering and Simulation Methods · Stochastic processes and financial applications