This article is devoted to the peculiarities of the application of cumulative theory of prospectuses to identify the degree of risk decisions in the implementation of projects in the field of high-tech innovations. In the theoretical part of the article, the authors note that obtaining an assessment of the degree of efficiency of investments in various large innovative projects is a rather laborious and complex process, in which a special place should be given to the analysis of the risk of the investments themselves. As an effective way to assess the level of risk present in the implementation of innovative projects, the authors of the article study the cumulative theory of the prospectuses, based on the theories of utility and management decision making, created by Daniel Kaneman and Amos Tversky. Furthermore, the authors underline that if the administrative decision is accepted in the conditions of uncertainty, it should necessarily consider various psychological factors in comparison with classical models of decision-makin, which are constructed on conditions of the maximum availability of the information. In the research part of article, the authors consider a way of an estimation of integral risks of innovative projects. In the final part of article, the authors come to the conclusions that the algorithm of an estimation of risks of innovative projects should obligatory include, not only an expert estimation at an initial stage, but also the subsequent adjustment of the values received after the decision taken regarding the optimization problems.