Portfolio optimization under downside risk is of crucial importance to asset managers. In this article we consider one such particular measure given by the notion of Capital at Risk (CaR), closely related to Value at Risk. We consider portfolio optimization with respect to CaR in the...

This paper derives explicit closed form solutions, for the efficient frontier and optimal investment strategy, for the dynamic mean-variance portfolio selection problem under the constraint of a higher borrowing rate. The method used is the Hamilton-Jacobi-Bellman (HJB) equation in a stochastic...