Related papers: Trading activity as driven Poisson process: compar…
Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid.…
We consider stochastic processes arising from dynamical systems simply by evaluating an observable function along the orbits of the system and study marked point processes associated to extremal observations of such time series…
Generalized evolutionary point processes offer a class of point process models that allows for either excitation or inhibition based upon the history of the process. In this regard, we propose modeling which comprises generalization of the…
We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise…
In this paper, we develop two stochastic models where the variable under consideration follows Harris distribution. The mean and variance of the processes are derived and the processes are shown to be non-stationary. In the second model,…
The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
This article considers a model for alternative processes for securities prices and compares this model with actual return data of several securities. The distributions of returns that appear in the model can be Gaussian as well as…
Define the scaled empirical point process on an independent and identically distributed sequence $\{Y_i: i\le n\}$ as the random point measure with masses at $a_n^{-1} Y_i$. For suitable $a_n$ we obtain the weak limit of these point…
Living systems often function with regulatory interactions, but the question of how activity, stochasticity and regulations work together for achieving different goals still remains puzzling. We propose a stochastic model of an active…
We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…
We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real…
We carry out a large-scale empirical data analysis to examine the efficiency of the so-called pairs trading. On the basis of relevant three thresholds, namely, starting, profit-taking, and stop-loss for the `first-passage process' of the…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
We propose a simple stochastic model of market behavior. Dividing market participants into two groups: trend-followers and fundamentalists, we derive the general form of a stochastic equation of market dynamics. The model has two…
This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…
A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process…
Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has…