Optimization models require continuous constraints to converge. However, some real-life problems are better described by models that incorporate discontinuous constraints. A common type of such discontinuous constraints becomes apparent when a regulation-mandated diversification requirement is implemented in an investment portfolio model. Generally stated, the requirement postulates that the aggregate of investments with individual weights exceeding certain threshold in the portfolio should not exceed some predefined total within the portfolio. This format of the diversification requirement can be defined by the rules of any specific portfolio construction methodology and is commonly imposed by the regulators.
The paper discusses the impact of this type of discontinuous portfolio diversification constraint on the portfolio optimization model solution process, and develops a convergent approach. The latter includes a sequence of definite series of convergent non-linear optimization problems and is presented in the framework of the OPTMODEL procedure modeling environment. The approach discussed has been used in constructing investable equity indexes.
Taras Zlupko and Robert Spatz from the University of Chicago presented on this topic during SAS Global Forum 2016. Click here to read their presentation.