Short texts are omnipresent in real-time news, social network commentaries, etc. Traditional text representation methods have been successfully applied to self-contained documents of medium size. However, information in short texts is often insufficient, due, for example, to the use of mnemonics, which makes them hard to classify. Therefore, the particularities of specific domains must be exploited. In this article we describe a novel system that combines Natural Language Processing techniques with Machine Learning algorithms to classify banking transaction descriptions for personal finance management, a problem that was not previously considered in the literature. We trained and tested that system on a labelled dataset with real customer transactions that will be available to other researchers on request. Motivated by existing solutions in spam detection, we also propose a short text similarity detector to reduce training set size based on the Jaccard distance. Experimental results with a two-stage classifier combining this detector with a SVM indicate a high accuracy in comparison with alternative approaches, taking into account complexity and computing time. Finally, we present a use case with a personal finance application, CoinScrap, which is available at Google Play and App Store.