Patent ID: 7630930

Claim:
A program storage device readable by a computer having a processor and a memory, tangibly embodying a program of instructions which when executed by the processor causes the processor to perform a method for optimizing a portfolio of a finite number n of assets, said method comprising the steps of: storing in the memory of the computer a belief matrix D from one or more relationships between the expected returns r=r 1 , r 2 , r 3 . . . r n of the assets; generating by the computer processor of the computer asset returns that are consistent with the belief matrix D to form a consistent set Q of return vectors; generating by the computer processor of the computer a centroid vector c of the consistent set Q of return vectors with respect to a probability measure h; and determining by the computer processor of the computer an optimal portfolio by finding a weight vector w=(w 1 , w 2 , w 3 . . . w n )that maximizes a vector relationship with the centroid vector c, wherein the one or more relationships are one or more linear homogeneous inequalities between the expected returns r of the form D i1 r 1 +D i2 r 2 + . . . +D in r n ≧0, where D ij are entries of the belief matrix D, where 1≦i≦M and 1≦j≦N, and M and N are finite, natural numbers, the consistent set Q of return vectors is given by Q={rεR N |Dr≧ 0}, the centroid vector c is given by c = ∫ r ∈ Q ⁢ r ⁢ ⅆ h , and the vector relationship between the weight vector w and the centroid vector c is an inner product, w·c.