An analytical derivation of the efficient surface in portfolio selection with three criteria

摘要: In standard mean-variance bi-criterion portfolio selection, the efficient set is a frontier. While it not yet for there to be additional criteria in has been growing amount of discussion literature on topic. However, should even one criterion, frontier becomes an surface. Striving parallel Merton’s seminal analytical derivation frontier, this paper we provide surface when linear criterion (on top expected return and variance) included model addressed by Merton. Among results is, as higher dimensional counterpart 2-mutual-fund theorem traditional 3-mutual-fund tri-criterion selection. 3D graphs are employed stress paraboloidic/hyperboloidic structures present