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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

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

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

Tirole (1985) studied an overlapping generations model with capital accumulation and showed that the emergence of asset bubbles solves the capital over-accumulation problem. His Proposition 1(c) claims that if the dividend growth rate is…

Theoretical Economics · Economics 2026-05-22 Ngoc-Sang Pham , Alexis Akira Toda

We revisit the classic paper of Tirole "Asset Bubbles and Overlapping Generations" (1985, Econometrica), which shows that the emergence of asset bubbles solves the capital over-accumulation problem. While Tirole's main insight holds with…

Theoretical Economics · Economics 2026-01-29 Ngoc-Sang Pham , 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

This paper studies the dividend and capital injection problem under a diffusion risk model with general discount functions. A proportional cost is imposed when injecting capitals. For exponential discounting as time-consistent benchmark, we…

Mathematical Finance · Quantitative Finance 2025-05-30 Sang Hu , Zihan Zhou

This paper develops a dynamic equilibrium model where agents exhibit a strong form of belief heterogeneity: they disagree about zero probability events. It is shown that, somewhat surprisingly, equilibrium exists in this setting, and that…

General Finance · Quantitative Finance 2013-06-24 Martin Larsson

We analyze how equilibrium housing prices are determined in the process of economic development within an overlapping generations model with perfect housing and rental markets. We characterize the rent growth rate in all equilibria. The…

Theoretical Economics · Economics 2025-05-09 Tomohiro Hirano , Alexis Akira Toda

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

We construct continuous-time equilibrium models based on a finite number of exponential utility investors. The investors' income rates as well as the stock's dividend rate are governed by discontinuous Levy processes. Our main result…

Mathematical Finance · Quantitative Finance 2015-07-14 Kasper Larsen , Tanawit Sae Sue

We study and generalize in various ways the model of rational expectation (RE) bubbles introduced by Blanchard and Watson in the economic literature. First, bubbles are argued to be the equivalent of Goldstone modes of the fundamental…

Statistical Mechanics · Physics 2009-11-07 D. Sornette , Y. Malevergne

We present a general equilibrium macro-finance model with a positive feedback loop between capital investment and land price. As leverage is relaxed beyond a critical value, through the financial accelerator, a phase transition occurs from…

Theoretical Economics · Economics 2024-02-15 Tomohiro Hirano , Ryo Jinnai , 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 equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes.…

Computer Science and Game Theory · Computer Science 2014-06-04 Shahar Dobzinski , Michal Feldman , Inbal Talgam-Cohen , Omri Weinstein

We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are…

Optimization and Control · Mathematics 2019-07-24 Jussi Keppo , Max Reppen , H. Mete Soner

In this paper we further extend the optimal bubble riding model proposed by Tangpi and Wang by allowing for price-dependent entry times. Agents are characterized by their individual entry threshold that represents their belief in the…

Mathematical Finance · Quantitative Finance 2025-11-04 Ludovic Tangpi , Shichun Wang

This paper studies a continuous-time portfolio selection problem under a general distribution of random risk aversion (RRA). We provide a complete characterization of all deterministic equilibrium strategies in closed form. Our results show…

Mathematical Finance · Quantitative Finance 2026-02-02 Weilun Cheng , Zongxia Liang , Sheng Wang , Jianming Xia

Recent financial bubbles such as the emergence of cryptocurrencies and "meme stocks" have gained increasing attention from both retail and institutional investors. In this paper, we propose a game-theoretic model on optimal liquidation in…

Mathematical Finance · Quantitative Finance 2024-02-02 Ludovic Tangpi , Shichun Wang

This paper provides a general characterization of subgame perfect equilibria for strategic timing problems, where two firms have the (real) option to make an irreversible investment. Profit streams are uncertain and depend on the market…

Economics · Quantitative Finance 2018-05-23 Jan-Henrik Steg
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