Global optimisation of a portfolio adjustment problem under credibility measures

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.