Evolutionary Stochastic Portfolio Optimization

In this chapter, the concept of evolutionary stochastic portfolio optimization is discussed. Selected theory from the fields of Stochastic Programming, evolutionary computation, portfolio optimization, as well as financial risk management is used to derive a generalized framework for computing optimal financial portfolios given an uncertain future using a probabilistic risk measure approach. A set of structurally different risk measures - Standard Deviation, Mean-absolute Downside Semi Deviation, Value-at-Risk, and Expected Shortfall - which are commonly used for practical portfolio management purposes have been selected to substantiate the approach with numerical results.

[1]  Ken-ichi Tokoro A statistical selection mechanism of GA for stochastic programming problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[2]  Minqiang Li,et al.  A Genetic Algorithm for Solving Portfolio Optimization Problems with Transaction Costs and Minimum Transaction Lots , 2005, ICNC.

[3]  Anthony Brabazon,et al.  Biologically inspired algorithms for financial modelling , 2006, Natural computing series.

[4]  Kathrin Klamroth,et al.  An MCDM approach to portfolio optimization , 2004, Eur. J. Oper. Res..

[5]  P. Embrechts,et al.  Chapter 8 – Modelling Dependence with Copulas and Applications to Risk Management , 2003 .

[6]  P. Krokhmal,et al.  Portfolio optimization with conditional value-at-risk objective and constraints , 2001 .

[7]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[8]  R. Rockafellar,et al.  Generalized Deviations in Risk Analysis , 2004 .

[9]  George B. Dantzig,et al.  Linear Programming Under Uncertainty , 2004, Manag. Sci..

[10]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[11]  Sebastian Engell,et al.  A hybrid evolutionary algorithm for solving two-stage stochastic integer programs in chemical batch scheduling , 2007, Comput. Chem. Eng..

[12]  Ronald Hochreiter,et al.  An Evolutionary Computation Approach to Scenario-Based Risk-Return Portfolio Optimization for General Risk Measures , 2009, EvoWorkshops.

[13]  Michael O'Neill,et al.  Biologically Inspired Algorithms for Financial Modelling (Natural Computing Series) , 2005 .

[14]  Andreas Zell,et al.  Evolutionary Algorithms and the Cardinality Constrained Portfolio Optimization Problem , 2004 .

[15]  William T. Ziemba,et al.  Applications of Stochastic Programming , 2005 .

[16]  Peter Kall,et al.  Stochastic Programming , 1995 .

[17]  Ronald Hochreiter,et al.  Financial scenario generation for stochastic multi-stage decision processes as facility location problems , 2007, Ann. Oper. Res..

[18]  Gary G. Yen,et al.  A generic framework for constrained optimization using genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

[19]  Manfred Gilli,et al.  A Data-Driven Optimization Heuristic for Downside Risk Minimization , 2006 .

[20]  R. Tyrrell Rockafellar,et al.  Coherent Approaches to Risk in Optimization Under Uncertainty , 2007 .

[21]  G. Pflug,et al.  Modeling, Measuring and Managing Risk , 2008 .

[22]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[23]  Andreas Zell,et al.  Comparing Discrete and Continuous Genotypes on the Constrained Portfolio Selection Problem , 2004, GECCO.

[24]  Carlos A. Coello Coello,et al.  THEORETICAL AND NUMERICAL CONSTRAINT-HANDLING TECHNIQUES USED WITH EVOLUTIONARY ALGORITHMS: A SURVEY OF THE STATE OF THE ART , 2002 .

[25]  E. Beale ON MINIMIZING A CONVEX FUNCTION SUBJECT TO LINEAR INEQUALITIES , 1955 .

[26]  Kaisa Miettinen,et al.  Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms , 2003, J. Glob. Optim..

[27]  H. Wee,et al.  Non-linear Stochastic Optimization Using Genetic Algorithm for Portfolio Selection , 2006 .

[28]  María Auxilio Osorio Lama,et al.  Hybrid search for cardinality constrained portfolio optimization , 2006, GECCO '06.

[29]  Piero P. Bonissone,et al.  Multiobjective financial portfolio design: a hybrid evolutionary approach , 2005, 2005 IEEE Congress on Evolutionary Computation.

[30]  Andreas Zell,et al.  Evaluating a hybrid encoding and three crossover operators on the constrained portfolio selection problem , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[31]  Christian Blum,et al.  Metaheuristics in combinatorial optimization: Overview and conceptual comparison , 2003, CSUR.

[32]  Teemu Pennanen,et al.  Epi-convergent discretizations of stochastic programs via integration quadratures , 2005, Numerische Mathematik.

[33]  Stan Uryasev,et al.  Conditional value-at-risk: optimization algorithms and applications , 2000, Proceedings of the IEEE/IAFE/INFORMS 2000 Conference on Computational Intelligence for Financial Engineering (CIFEr) (Cat. No.00TH8520).

[34]  Dietmar Maringer,et al.  Portfolio management with heuristic optimization , 2005 .

[35]  Detlef Seese,et al.  A Multi-objective Approach to Integrated Risk Management , 2005, EMO.

[36]  Sebastian Engell,et al.  Design of problem-specific evolutionary algorithm/mixed-integer programming hybrids: two-stage stochastic integer programming applied to chemical batch scheduling , 2007 .