, Volume 193, Issue 1, pp 129-158
Date: 30 Mar 2011

Heuristic optimisation in financial modelling

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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 (e.g., 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.

This paper builds on an invited lecture by Manfred Gilli at the APMOD 2008 conference in Bratislava, Slovakia. The authors would like to thank the conference organisers, in particular Georg Pflug and Ronald Hochreiter, and participants of the session. Both authors also gratefully acknowledge financial support from the EU Commission through MRTN-CT-2006-034270 COMISEF.