An optimization model of the portfolio adjusting problem with fuzzy return and a SMO algorithm

Based on possibilistic mean and variance theory, this paper deals with the portfolio adjusting problem for an existing portfolio under the assumption that the returns of risky assets are fuzzy numbers and there exist transaction costs in portfolio adjusting precess. We propose a portfolio optimization model with V-shaped transaction cost which is associated with a shift from the current portfolio to an adjusted one. A sequential minimal optimization (SMO) algorithm is developed for calculating the optimal portfolio adjusting strategy. The algorithm is based on deriving the shortened optimality conditions for the formulation and solving 2-asset sub-problems. Numerical experiments are given to illustrate the application of the proposed model and the efficiency of algorithm. The results also show clearly the influence of the transaction costs in portfolio selection.