About the variation approach to models of the portfolio investment

Abstract

We consider permanent dynamic analog models of Markowitz and To-bin about optimizing portfolio of assets for a period of time, using an integral criterion for the effectiveness of the portfolio. Special atten¬tion was paid on the objective of maximizing portfolio returns with limited risk. Owing to the nature of the problem, used a variation approach allows us to obtain results in many respects similar to the classical stationary case, in particular, write down the formula for the solutions explicitly. Some results are new even for classical problems of Markowitz and Tobin.