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This article provides a self-contained overview of the theory of rational asset price bubbles. We cover topics from basic definitions, properties, and classical results to frontier research, with an emphasis on bubbles attached to real…

General Economics · Economics 2024-02-05 Tomohiro Hirano , Alexis Akira Toda

The price-bubble and crash process formation is theoretically investigated in a two-asset equilibrium model. Sufficient and necessary conditions are derived for the existence of average equilibrium price dynamics of different agent-based…

Trading and Market Microstructure · Quantitative Finance 2024-09-06 Francesco Cordoni

Emerging markets such as India provide investors with returns far greater than those in developed markets; taking the average returns from the period 1995 to 2014 the returns are 4.714% to 3.276% of the developed market. The majority of…

General Finance · Quantitative Finance 2022-07-28 Ganapathy G Gangadharan , N. Suresh

We construct a statistical indicator for the detection of short-term asset price bubbles based on the information content of bid and ask market quotes for plain vanilla put and call options. Our construction makes use of the martingale…

Pricing of Securities · Quantitative Finance 2018-07-17 Petteri Piiroinen , Lassi Roininen , Tobias Schoden , Martin Simon

Asset price bubbles are situations where asset prices exceed the fundamental values defined by the present value of dividends. This paper presents a conceptually new perspective: the necessity of bubbles. We establish the Bubble Necessity…

Theoretical Economics · Economics 2024-08-12 Tomohiro Hirano , Alexis Akira Toda

In this study, we investigate asset price bubbles in a discrete-time, discrete-state market under model uncertainty and short sales prohibitions. Building on a new fundamental theorem of asset pricing and a superhedging duality in this…

Mathematical Finance · Quantitative Finance 2025-12-25 Wenqing Zhang

We study asset price bubbles in market models with proportional transaction costs $\lambda\in (0,1)$ and finite time horizon $T$ in the setting of [49]. By following [28], we define the fundamental value $F$ of a risky asset $S$ as the…

Mathematical Finance · Quantitative Finance 2020-12-09 Francesca Biagini , Thomas Reitsam

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-independent. We test the accuracy of our methodology in numerical…

Mathematical Finance · Quantitative Finance 2024-06-21 Francesca Biagini , Lukas Gonon , Andrea Mazzon , Thilo Meyer-Brandis

We consider a simple stochastic differential equation for modeling bubbles in social context. A prime example is bubbles in asset pricing, but similar mechanisms may control a range of social phenomena driven by psychological factors (for…

General Finance · Quantitative Finance 2010-09-03 Alexander Kiselev , Lenya Ryzhik

Episodes of market crashes have fascinated economists for centuries. Although many academics, practitioners and policy makers have studied questions related to collapsing asset price bubbles, there is little consensus yet about their causes…

Risk Management · Quantitative Finance 2008-12-15 T. Kaizoji , D. Sornette

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…

General Economics · Economics 2025-02-17 Michael Heinrich Baumann , Anja Janischewski

Considering a simple economy, we derive a new Hamilton-Jacobi equation which is satisfied by the value of a ''bubble'' asset. We then show, by providing a rigorous mathematical analysis of this equation, that a unique non-zero stable…

Analysis of PDEs · Mathematics 2025-05-22 Charles Bertucci , Jean-Michel Lasry , Pierre Louis Lions

A rational bubble is a situation in which the asset price exceeds its fundamental value defined by the present discounted value of dividends in a rational equilibrium model. We discuss the recent development of the theory of rational…

Theoretical Economics · Economics 2025-09-03 Tomohiro Hirano , Alexis Akira Toda

There is a growing concern in recent years over the potential formation of bubbles in the Chinese real estate market. This paper aims to conduct a series of bubble diagnostic analysis over nine representative Chinese cities from two…

Risk Management · Quantitative Finance 2018-01-12 Tianhao Zhi , Zhongfei Li , Zhiqiang Jiang , Lijian Wei , Didier Sornette

Identifying unambiguously the presence of a bubble in an asset price remains an unsolved problem in standard econometric and financial economic approaches. A large part of the problem is that the fundamental value of an asset is, in…

General Finance · Quantitative Finance 2010-11-25 Wanfeng Yan , Ryan Woodard , Didier Sornette

We study an overlapping generations (OLG) exchange economy with an asset that yields dividends. First, we derive general conditions, based on exogenous parameters, that give rise to three distinct scenarios: (1) only bubbleless equilibria…

Computational Finance · Quantitative Finance 2025-09-03 Stefano Bosi , Cuong Le Van , Ngoc-Sang Pham

We introduce a new diffusion process Xt to describe asset prices within an economic bubble cycle. The main feature of the process, which differs from existing models, is the drift term where a mean-reversion is taken based on an exponential…

Mathematical Finance · Quantitative Finance 2018-03-23 Angelos Dassios , Luting Li

Establishing unambiguously the existence of speculative bubbles is an on-going controversy complicated by the need of defining a model of fundamental prices. Here, we present a novel empirical method which bypasses all the difficulties of…

Statistical Mechanics · Physics 2015-06-24 B. M. Roehner , D. Sornette

We highlight a very simple statistical tool for the analysis of financial bubbles, which has already been studied in [1]. We provide extensive empirical tests of this statistical tool and investigate analytically its link with stocks…

Statistical Finance · Quantitative Finance 2009-09-17 Frederic Abergel , Nicolas Huth , Ioane Muni Toke

We define and study a rather complex market model, inspired from the Santa Fe artificial market and the Minority Game. Agents have different strategies among which they can choose, according to their relative profitability, with the…

Condensed Matter · Physics 2009-11-07 Irene Giardina , Jean-Philippe Bouchaud
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