Solving Portfolio Optimization Problems Using AMPL

Abstract

This work presents a new optimization software library which contains a number of financial optimization models. Roughly speaking, the majority of these portfolio allocation models aim to compute the optimal allocation investment weights, and thus they are particularly useful for supporting investment decisions in financial markets. Algebraic modeling languages are very well suited for prototyping and developing optimization models. All the financial optimization models have been implemented in AMPL mathematical programming modeling language and solved using either Gurobi Optimizer or Knitro (for those models having general nonlinear objectives). This proposed software library includes several well-known portfolio allocation models, such as the Markowitz mean-variance model, the Konno-Yamazaki absolute deviation model, the Black-Litterman model, Young’s minimax model and others. These models aim either to minimize the variance of the portfolios, or maximize the expected returns subject to a number of constraints, or include portfolios with a risk-free asset, transaction costs, and others. Furthermore, we also present a literature review of financial optimization software packages and discuss the benefits and drawbacks of our proposed portfolio allocation model library. Since this is a work in progress, new models are still being added to the proposed library.