An Uncertain Risk Index Model for Multi-Period Portfolio Selection

This paper discusses a multi-period portfolio problem in the situation where security returns are given mainly by experts' judgment and evaluation. The security return rates are regarded as uncertain variables in the situation and the justification of using them is discussed. An uncertain adjusting Risk Index model is proposed in which optimal portfolio adjustments are determined with the objective of minimizing a cumulative Risk Index over the investment horizon, while satisfying self-financing constraints at each period and achieving a desired incremental wealth target. The adjusting model is converted into its crisp form, enabling the users to effectively solve the multi-period adjusting problem with currently available programming solvers. For the sake of illustration, an example is also provided.