Differential Evolution (DEoptim) for Non-Convex Portfolio Optimization

Ardia, David and Boudt, Kris and Carl, Peter and Mullen, Katharine M. and Peterson, Brian (2010): Differential Evolution (DEoptim) for Non-Convex Portfolio Optimization.

Abstract

The R package DEoptim implements the differential evolution algorithm. This algorithm is an evolutionary technique similar to genetic algorithms that is useful for the solution of global optimization problems. In this note we provide an introduction to the package and demonstrate its utility for financial applications by solving a non-convex portfolio optimization problem.

• Item Type: MPRA Paper
• Language: English
• Keywords: Differential optimization; non-convex portfolio optimization; DEoptim; R software
• Subjects: G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

Ardia, D. & Mullen, K. (2009), 'DEoptim: Differential Evolution Optimization in R', R package version 2.00-04.

Börner, J.; Higgins, S. I.; Kantelhardt, J. & Scheiter, S. (2007), 'Rainfall or Price Variability: What Determines Rangeland Management Decisions? A Simulation-Optimization Approach to South African Savanas', Agricultural Economics 37(2--3), 189-200.

Boudt, K.; Carl, P. & Peterson, B. G. (2010), 'Portfolio Optimization with Conditional Value-at-Risk Budgets'.

Boudt, K.; Carl, P. & Peterson, B. G. (2010), 'PortfolioAnalytics: Portfolio Analysis, including Numeric Methods for Optimization of Portfolios', R package version 0.3.

Carl, P. & Peterson, B. G. (2009), 'PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis in R', R package version 1.0.0.

Gilli, M.; Maringer, D. G. & Winker, P. (2008), Applications of Heuristics in Finance, in Detlef Schlottmann; Christof Weinhardt & Frank Schlottmann, ed.,'Handbook on Information Technology in Finance', Springer-Verlag, Berlin, Heidelberg.

Gilli, M. & Schumann, E. (2009), 'Heuristic Optimisation in Financial Modelling', COMISEF wps-007 09/02/2009.

Gilli, M. & Winker, P. (2008), 'A Review of Heuristic Optimization Methods in Econometrics', Swiss Institute Research paper series 08-12.

Higgins, S. I.; Kantelhardt, J.; Scheiter, S. & Börner, J. (2007), 'Sustainable Management of Extensively Managed Savanna Rangelands', Ecological Economics 62(1), 102-114. Holland, J. H. (1975), Adaptation in Natural Artificial Systems, University of Michigan Press, Ann Arbor.

Krink, T.; Mittnik, S. & Paterlini, S. (2009), 'Differential Evolution and Combinatorial Search for Constrained Index-Tracking', Annals of Operations Research 172, 153-176.

Krink, T. & Paterlini, S. (2009), 'Multiobjective Optimization using Differential Evolution for Real-World Portfolio Optimization', Computational Management Science.

Lampinen, J. A. (2009), 'A Bibliography of Differential Evolution Algorithm'.

Maringer, D. G. (2005), Portfolio Management with Heuristic Optimization'Advanced in Computational Management Science', Springer-Verlag, .

Maringer, D. G. & Meyer, M. (2008), 'Smooth Transition Autoregressive Models: New Approaches to the Model Selection Problem', Studies in Nonlinear Dynamics & Econometrics 12(1), 1-19.

Maringer, D. G. & Oyewumi, O. (2007), 'Index Tracking with Constrained Portfolios', Intelligent Systems in Accounting, Finance & Management 15(1--2), 57-71. Mitchell, M. (1998), An Introduction to Genetic Algorithms, The MIT Press.

Mullen, K. M.; Ardia, D.; Gil, D. L.; Windover, D. & Cline, J. (2009), 'DEoptim: An R Package for Global Optimization by Differential Evolution'.

Opsina Arango, J. D. (2009), 'Estimacion de un Modelo de Difusion con Saltos con Distribucion de Error Generalizada Asimetrica usando Algorithmos Evolutivos', Master's thesis, Universidad Nacional de Colombia.

Price, K. V.; Storn, R. M. & Lampinen, J. A. (2006), Differential Evolution: A Practical Approach to Global Optimization, Springer-Verlag, Berlin, Germany.

Scaillet, O. (2002), 'Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall', Mathematical Finance 14(1), 74-86.

Storn, R. & Price, K. (1997), 'Differential Evolution -- A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces', Journal of Global Optimization 11(4), 341-359.

Yollin, G. (2009), 'R Tools for Portfolio Optimization''Presentation at R/Finance conference 2009'.