An Uncertain Risk Index Model for the Constrained Portfolio Adjusting Problem

This paper discusses a portfolio adjusting problem with additional risk assets and a riskless asset in the situation where risk asset returns are regarded as uncertain variables. Using expected value and risk index as measures of return and risk, we propose a portfolio optimization model for an existing portfolio with transaction costs, bounded constraints and minimum transaction lots on holding of risk assets. Besides, we also consider the fact that the riskless asset (capital) can be borrowed or lent at different interest rates. The adjusting model is converted into its crisp form, enabling the users to effectively solve the adjusting problem with currently available programming solvers. For the sake of illustration, an example is also provided.