Abstract: There exist frictions such as transaction costs,taxes in stock market.The investors will be affected by these frictions in their investment decision.In this paper,we propose a mathematical model for optimal portfolio selection problem with market frictions,using investors maximal utility as objective function.We also discuss the portfolio selection model which includes market frictions and short sales.This model can be formulated as a convex quadratic programming problem.We propose a path-following algorithm for solving this model.

Key words: quadratic programming, friction market, short sales.