"If you want to understand the bewildering complexity of consumer markets, financial markets and beyond, the traditional textbooks or theories wouldn't help much. This book presents a new market theory in which information plays the most important role. We portray the markets with three...

In this paper, we introduce a modified collaborative filtering (MCF) algorithm, which has remarkably higher accuracy than the standard collaborative filtering. In the MCF, instead of the cosine similarity index, the user–user correlations are obtained by a diffusion process. Furthermore, by...

Recommender systems use data on past user preferences to predict possible future likes and interests. A key challenge is that while the most useful individual recommendations are to be found among diverse niche objects, the most reliably accurate results are obtained by methods that recommend...

We study the risk criterion for investments based on the drawdown from the maximal value of the capital in the past. Depending on investor's risk attitude, thus his risk exposure, we find that the distribution of these drawdowns follows a general power law. In particular, if the risk exposure is...