A comprehensive approach to the optimization of financial portfolios is provided by the Integral Analysis Method (IAM), which comprises four steps: The description of the problem is followed by three mathematical steps, namely, cardinal analysis, ordinal analysis and integration analysis, which allow simultaneously involving ordinal and cardinal variables in an optimization problem. The cardinal analysis uses the L_1 risk model, which is enriched by the inclusion of a stochastic constraint on the successful performance forecast attributed to each of the shares that make up the investment portfolio. This bound, however, does not alter the linear nature of the model. The Ordinal analysis includes expert opinions on the reputation of each company as a qualitative criterion. This completes two of the most relevant aspects of the investment portfolio optimization problem: success probability (assessed through the cardinal analysis) and business reputation (assessed through the ordinal analysis). By resorting to Stochastic Multicriteria Acceptability Analysis, the integration analysis allows obtaining indicators that jointly evaluate the variables resulting from the two previous analyses. As a validation process, IAM was applied to simulated data.