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Heuristic Optimisation in Financial Modelling

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  • Manfred Gilli
  • Enrico Schumann

Abstract

There is a large number of optimisation problems in theoretical and applied finance that are difficult to solve as they exhibit multiple local optima or are not ‘well- behaved’ in other ways (eg, discontinuities in the objective function). One way to deal with such problems is to adjust and to simplify them, for instance by dropping constraints, until they can be solved with standard numerical methods. This paper argues that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable to handle non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, the paper presents several actual problems where classical methods fail. Next, several well-known heuristic techniques that may be deployed in such cases are described. Since such presentations are quite general, the paper describes in some detail how a particular problem, portfolio selection, can be tackled by a particular heuristic method, Threshold Accepting. Finally, the stochastics of the solutions obtained from heuristics are discussed. It is shown, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computations.

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  • Manfred Gilli & Enrico Schumann, 2009. "Heuristic Optimisation in Financial Modelling," Working Papers 007, COMISEF.
  • Handle: RePEc:com:wpaper:007
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    References listed on IDEAS

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    1. Manfred Gilli & Enrico Schumann, "undated". "Distributed Optimisation of a Portfolio's Omega," Swiss Finance Institute Research Paper Series 08-17, Swiss Finance Institute.
    2. Gilli, M. & Winker, P., 2003. "A global optimization heuristic for estimating agent based models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 299-312, March.
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    Cited by:

    1. Gaudard, Ludovic, 2015. "Pumped-storage project: A short to long term investment analysis including climate change," Renewable and Sustainable Energy Reviews, Elsevier, vol. 49(C), pages 91-99.
    2. repec:eee:ejores:v:263:y:2017:i:2:p:625-638 is not listed on IDEAS
    3. Jevtić, Petar & Luciano, Elisa & Vigna, Elena, 2013. "Mortality surface by means of continuous time cohort models," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 122-133.
    4. Ardia, David & Boudt, Kris & Carl, Peter & Mullen, Katharine M. & Peterson, Brian, 2010. "Differential Evolution (DEoptim) for Non-Convex Portfolio Optimization," MPRA Paper 22135, University Library of Munich, Germany.
    5. Billio, Monica & Caporin, Massimiliano & Costola, Michele, 2015. "Backward/forward optimal combination of performance measures for equity screening," The North American Journal of Economics and Finance, Elsevier, vol. 34(C), pages 63-83.
    6. repec:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-016-2111-x is not listed on IDEAS

    More about this item

    Keywords

    Optimisation heuristics; Financial Optimisation; Portfolio Optimisation;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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