Financial bubbles and crashes have repeatedly caused economic turmoil notably but not only during the 2008 financial crisis. However, both in the popular press as well as scientific publications, the meaning of bubble is sometimes unspecified. Due to the multitude of bubble definitions, we...

Deviation of an asset price from its fundamental value, commonly referred to as a price bubble, is a well-known phenomenon in financial markets. Mathematically, a bubble arises when the deflated price process transitions from a martingale to a strict local martingale. This paper explores price...

This paper aims to develop optional semimartingale methods in risk theory to allow for a larger class of risk models. Optional semimartingales are left-continuous with right-limit stochastic processes defined on a probability space where the usual conditions - completeness and right-continuity...

This paper focuses on the task of detecting local episodes involving violation of the standard Itô semimartingale assumption for financial asset prices in real time that might induce arbitrage opportunities. Our proposed detectors, defined as stopping rules, are applied sequentially to...