To transform it into DEA efficient, on the basis of findng out some efficient frontier hyperplanes nearby (X 0, Y 0), this paper gives a method on minimzing the sum of deviations in output and input between (X 0,Y 0) and any point lying on these efficient frontier hyperplanes.

Research on the M-V efficient frontier as the security number changes;

Study on the M-V efficient frontier with non-risk assets;

Optimization of Portfolio:Efficient Frontier under Saving/Borrowing Rates Spread;

We obtain a complete computational method of the effective frontier as follows:①If speculation is not allowed,then the effective frontier is the hyperbola segment S 1S 2 when ρ 12≥σ 1σ 2,and the effective frontier is the hyperbola segment CS 2 when ρ 12<σ 1σ 2.

Using functional analysis theory,this paper proves the existence of the portfolio effective frontier under random vector Hilbert space.

An analysis of the substitution rate of annuity and its corresponding investment risks and ratios can be made in accordance with the historical performance of closed funds through the portfolio effective frontier approach, indicating the upper limits of trust costs and performance management expenses and providing a decision-making approach.

Solving the model step by step,some efficient portfolio was gained and the efficient frontier curve was simulated.