An algebraic theory of portfolio allocation (Q1407777)

This paper explores the portfolio allocation from the algebraic theory perspective. The optimal portfolio is defined as maximizing the expected utility of the wealth. The authors assume that the vector of gross return follows some distribution function. The authors first define the action of the permutation group on the distribution function. Then he uses the group theory concepts such as transitivity of subgroup, point-wise stabilizer and group majorization to make constrains on the distribution function. They claim that if the distribution function satisfies some invariant properties under certain subgroup of the permutation group, then the optimal allocation must satisfy related properties. The authors established the optimal allocation of funds among assets when asymmetries in the return vector are carefully controlled.