Title: Global optimisation of a portfolio adjustment problem under credibility measures

Authors: Andreas Lundell; Kaj-Mikael Björk

Addresses: Center of Excellence in Optimisation and Systems Engineering, Åbo Akademi University, Turku, Finland ' Institute for Advanced Management Systems Research (IAMSR), Åbo Akademi University, Turku, Finland; Department of Business, Information Technology and Media, Arcada University of Applied Sciences, Helsinki, Finland

Abstract: In this paper it is shown how to find the guaranteed ε-optimal solution to the credibilistic portfolio adjustment problem in the formulation presented by Zhang et al. (2010). In its crisp form, the problem is a non-convex signomial programming problem. This type of problem is difficult to solve to global optimality and solving it using a non-global solver may give suboptimal solutions. Using the signomial global optimisation (SGO) algorithm, it is however possible to reformulate the problem into a convex problem whose feasible region overestimates that of the non-convex problem in an extended variable space. The overestimation is iteratively reduced until the global solution is found. To illustrate the procedure, the SGO algorithm is applied to the example in the original article. It is shown that the solutions presented were only local ones, and the global solution corresponding to better portfolio adjustment strategies is given.

Keywords: global optimisation; signomial functions; portfolio adjustment; possibility theory; credibility theory; credibility measures.

DOI: 10.1504/IJOR.2016.075292

International Journal of Operational Research, 2016 Vol.25 No.4, pp.464 - 474

Available online: 10 Mar 2016 *

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