Microblogging platforms, of which Twitter is a representative example, are valuable information sources for market screening and financial models. In them, users voluntarily provide relevant information, including educated knowledge on investments, reacting to the state of the stock markets in real-time and, often, influencing this state. We are interested in the user forecasts in financial, social media messages expressing opportunities and precautions about assets. We propose a novel Targeted Aspect-Based Emotion Analysis (TABEA) system that can individually discern the financial emotions (positive and negative forecasts) on the different stock market assets in the same tweet (instead of making an overall guess about that whole tweet). It is based on Natural Language Processing (NLP) techniques and Machine Learning streaming algorithms. The system comprises a constituency parsing module for parsing the tweets and splitting them into simpler declarative clauses; an offline data processing module to engineer textual, numerical and categorical features and analyse and select them based on their relevance; and a stream classification module to continuously process tweets on-the-fly. Experimental results on a labelled data set endorse our solution. It achieves over 90% precision for the target emotions, financial opportunity, and precaution on Twitter. To the best of our knowledge, no prior work in the literature has addressed this problem despite its practical interest in decision-making, and we are not aware of any previous NLP nor online Machine Learning approaches to TABEA.