Risk minimization and portfolio diversification
  We consider the problem of minimizing capital at risk in the Black-Scholes setting. The portfolio problem is studied given the possibility that a correlation constraint between the portfolio and a financial index is imposed. The optimal portfolio is obtained in closed form. The effects of the correlation constraint are explored; it turns out that this portfolio constraint leads to a more diversified portfolio. 
Farzad Pourbabaee, Minsuk Kwak and Traian A. Pirvu
q-fin.PM math.OC