Related papers: Market dynamics after large financial crash
This Chapter reviews statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the…
For the concrete model of Brownian particles dynamics in non-uniform environment, the time interval estimation is constructed, on which phenomenological Fick laws for diffusion phenomenon description can be used. The knowledge of these…
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 introduce a new notion of G-normal distributions. This will bring us to a new framework of stochastic calculus of Ito's type (Ito's integral, Ito's formula, Ito's equation) through the corresponding G-Brownian motion. We will also…
We study an optimal investment problem under contagion risk in a financial model subject to multiple jumps and defaults. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the…
The drift burst hypothesis postulates the existence of short-lived locally explosive trends in the price paths of financial assets. The recent U.S. equity and treasury flash crashes can be viewed as two high-profile manifestations of such…
A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…
We present a study on the dynamics of a system consisting of a pair of hardcore particles diffusing with different rates. We solved the drift-diffusion equation for this model in the case when one particle, labeled F, drifts and diffuses…
Proceeding from the concept of rational expectations, a new dynamic model of supply and demand in a single market with one supplier, one buyer, and one kind of commodity is developed. Unlike the cob-web dynamic theories with adaptive…
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary…
Sharp changes in time series representing market dynamics are studied by means of the self--similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous…
In the over-the-counter market in derivatives, we sometimes see large numbers of traders taking the same position and risk. When there is this kind of concentration in the market, the position impacts the pricings of all other derivatives…
An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…
We pursue the quantum-mechanical challenge to the efficient market hypothesis for the stock market by employing the quantum Brownian motion model. We utilize the quantum Caldeira-Leggett master equation as a possible phenomenological model…
In order to figure out and to forecast the emergence phenomena of social systems, we propose several probabilistic models for the analysis of financial markets, especially around a crisis. We first attempt to visualize the collective…
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…