VaR optimal portfolio with transaction costs

We consider the problem of portfolio optimization under VaR risk measure taking into account transaction costs. Fixed costs as well as impact costs as a nonlinear function of trading activity are incorporated in the optimal portfolio model. Thus the obtained model is a nonlinear optimization problem with nonsmooth objective function. The model is solved by an iterative method based on a smoothing VaR technique. We prove the convergence of the considered iterative procedure and demonstrate the nontrivial influence of transaction costs on the optimal portfolio weights.