This thesis is focused on a theoretical explanation of some models for the optimization stock portfolios with different risk measure. The theory of the nonlinear programming is detailed developed and also basic Markowitz`s model with another optimization models as Konno -- Yamazaki`s model, Roy`s model, semivariance approach and Value at Risk approach, which are based on alternative risk measure. For all models the assumptions of their applications are highlighted and the comparation of these models is made too. Analytical part is concerned in the construction of the effecient portfolios according to the described models is made on the historical market prices of 13 companies traded on Prague Stock Exchange in SPAD