We consider the risk minimization problem , with capital at risk as the coherent measure, under the Black-Scholes setting. The  problem is studied , when there exists additional correlation constraint between the desired portfolio and another financial index , and the closed form solution for the optimal portfolio is obtained . We also mention to variance reduction and getting better diversified portfolio as the applications of correlation condition in this paper .
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 .
R
risk minimization problem , with
problem of minimizing
R
as the coherent measure, under the
in the
A
portfolio
R
, when there exists additional
given the possibility that a
R
desired portfolio and another financial index , and the closed form solution for the
portfolio and a financial index is imposed. The
R
. We also mention to variance reduction and getting better diversified portfolio as the applications of correlation condition in this paper
in closed form. The effects of the correlation constraint are explored; it turns out that this portfolio constraint leads to a more diversified portfolio