Optimal portfolio of safety-first models

The purpose of this article is to study Kataoka's safety-first (KSF) model, which is a representative of safety-first models of most popular models in portfolio selection of modern finance. We obtain conditions that guarantee that the KSF model has a finite optimal solution without normality assumption. When short-sell is allowed, we provide an explicit analytical solution of the KSF model in two cases. When short-sell is not allowed, we propose an iterating algorithm for finding the optimal portfolios of the KSF model. We also investigate a KSF model with constraint of mean return and obtain the explicit analytical expression of the optimal portfolio.