This article reviews the theoretical literature on asset price bubbles, with an emphasis on the
martingale theory of bubbles. The key questions studied are as follows: First, under what …

Over the last 10 years or so a mathematical theory of bubbles has emerged, in the spirit of a
martingale theory based on an absence of arbitrage, as opposed to an equilibrium theory …

In the past decades, advanced probabilistic methods have had significant impact on the field
of finance, both in academia and in the financial industry. Conversely, financial questions …

At odds with the common “rational expectations” framework for bubbles, economists like
Hyman Minsky, Charles Kindleberger and Robert Shiller have documented that irrational …

We combine both a mathematical analysis of financial bubbles and a statistical procedure
for determining when a given stock is in a bubble, with an analysis of a large data set, in …

In this paper, we employ deep learning techniques to detect financial asset bubbles by using
observed call option prices. The proposed algorithm is widely applicable and model …

In a numéraire-independent framework, we study a financial market with N assets which are
all treated in a symmetric way. We define the fundamental value∗ S of an asset S as its …

A strict local martingale is a local martingale which is not a martingale. There are few explicit
examples of “naturally occurring” strict local martingales with jumps available in the …

This paper provides a bubble date‐stamping mechanism using the agent‐based
computational finance method. The key steps of the bubble date‐stamping mechanism are …

We study the formation of derivative prices in an equilibrium between risk-neutral agents
with heterogeneous beliefs about the dynamics of the underlying. Under the condition that …