Heuristic Optimisation in Financial Modelling

31 Pages Posted: 2 Oct 2008 Last revised: 14 Mar 2013

See all articles by Manfred Gilli

Manfred Gilli

University of Geneva - Research Center for Statistics; Swiss Finance Institute

Enrico Schumann

Independent

Date Written: October 16, 2010

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. We argue that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable of handling non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, we present 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, we then describe 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. We show, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computations.

Keywords: Optimisation heuristics, Financial Optimisation, Portfolio Optimisation

JEL Classification: C61, C63, G11

Suggested Citation

Gilli, Manfred and Schumann, Enrico, Heuristic Optimisation in Financial Modelling (October 16, 2010). Annals of Operations Research, Vol. 193, No. 1, pp. 129-158, 2012. Available at SSRN: https://ssrn.com/abstract=1277114

Manfred Gilli (Contact Author)

University of Geneva - Research Center for Statistics ( email )

Geneva
Switzerland
+41223798222 (Phone)
+41223798299 (Fax)

HOME PAGE: http://www.unige.ch/ses/metri/gilli/

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Enrico Schumann

Independent ( email )

No Address Available

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