In this paper, we draw upon the close relationship between statistical physics and mathematical finance to develop a suite of models for financial bubbles and crashes. By modifying previous approaches, we are able to derive novel analytical formulae for evaluation problems and for the expected...

There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the...

We propose a simple agent-based computational model in which speculators' trading behavior may cause bubbles and crashes, excess volatility, serially uncorrelated returns, fat-tailed return distributions and volatility clustering, thereby replicating five important stylized facts of stock...

Extreme events are ubiquitous in nature and social society, including natural disasters, accident disasters, crises in public health (such as Ebola and the COVID-19 pandemic), and social security incidents (wars, conflicts, and social unrest). These extreme events will heavily impact financial...

High-frequency financial data are characterized by a set of ubiquitous statistical properties that prevail with surprising uniformity. While these 'stylized facts' have been well-known for decades, attempts at their behavioral explanation have remained scarce. However, recently a new branch of...