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This article is one of the results obtained in a research project funded by EAFIT University in 2011, This paper is based upon a study carried out by Lacus and La Torre [1], it presents the fractal estimation through Iterated Function Systems (IFS), as an alternative to estimate the distribution function of added losses which is necessary to quantify the operational risk. As it is shown in the analysis, this technique can deal with some of the difficulties presented with some of the classic actuarial methodologies. Furthermore, an application is presented and conclusions are obtained from it. [ABSTRACT FROM AUTHOR]