Related papers: Multi-dimensional Rational Bubbles and fat tails: …
This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982), corresponding to multiplicative maps, whose study has recently be revived recently in physics as a mechanism of…
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…
We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by [Lux and Sornette, 1999] that the distribution of returns is a power law with exponent less than 1, in contradiction with…
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…
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…
We consider stochastic processes where randomly chosen particles with positive quantities x, y (> 0) interact and exchange the quantities asymmetrically by the rule x' = c{(1-a) x + b y}, y' = d{a x + (1-b) y} (x \ge y), where (0 \le) a, b…
Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-M\'ezard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes,…
We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails -- ubiquitous in the statistics of social, economic, and ecological systems. Our main…
Noncausal, or anticipative, heavy-tailed processes generate trajectories featuring locally explosive episodes akin to speculative bubbles in financial time series data. For $(X_t)$ a two-sided infinite $\alpha$-stable moving average (MA),…
The aim of this paper is to propose a heterogeneous agent model of stock markets that develop complicated endogenous price fluctuations. We find occurrences of non-stationary chaos, or speculative bubble, are caused by the heterogeneity of…
In retrospect, the experimental findings on competitive market behavior called for a revival of the old, classical, view of competition as a collective higgling and bargaining process (as opposed to price-taking behaviors) founded on…
Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
Economic and financial time series can feature locally explosive behavior when a bubble is formed. The economic or financial bubble, especially its dynamics, is an intriguing topic that has been attracting longstanding attention. To…
We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which rational investors and noise traders co-exist. Rational investors form expectations on the return and risk of a risky asset and…
Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…
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…
We study random design linear regression with no assumptions on the distribution of the covariates and with a heavy-tailed response variable. In this distribution-free regression setting, we show that boundedness of the conditional second…
We show that the quotient of Levy processes of jump-diffusion type has a fat-tailed distribution. An application is to price theory in economics. We show that fat tails arise endogenously from modeling of price change based on an excess…
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…