Abstract: In this paper, a new POTPL(POT-Power Law) model on the basis of fractal dimension theory by using POT model of extreme value theory is presented.It gives not only a theoretical explanation for the choice of the threshold of POT model, but also satisfying power law condition of estimating tail disfribution.The analysis result shows that this model can be more convenient to estimate the tail than former methods.And it provides a new idea for solving fat-tail problem in small-sample circumstances, In addition, the random sum model in insurance is introduced in order to solve calculating Sum VaR of the banking operational risk losses.Then a simplified formula of VaR is given on the basis of operational loss data in our banks.

Key words: fractal dimension, power law, POT model, random sum, VaR