Related papers: Trading activity as driven Poisson process: compar…
We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the true number of clusters is supposed to be known, a new…
We study a parsimonious but non-trivial model of the latent limit order book where orders get placed with a fixed displacement from a center price process, i.e.\ some process in-between best bid and best ask, and get executed whenever this…
We analyze the statistics of daily price change of stock market in the framework of a statistical physics model for the collective fluctuation of stock portfolio. In this model the time series of price changes are coded into the sequences…
A parametric point process model is developed, with modeling based on the assumption that sequential observations often share latent phenomena, while also possessing idiosyncratic effects. An alternating optimization method is proposed to…
In this paper we present an interacting-agent model of stock markets. We describe a stock market through an Ising-like model in order to formulate the tendency of traders getting to be influenced by the other traders' investment attitudes…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
Temporal point processes have been widely applied to model event sequence data generated by online users. In this paper, we consider the problem of how to design the optimal control policy for point processes, such that the stochastic…
Permutation tests have been proposed by Albert et al. (2015) to detect dependence between point processes, modeling in particular spike trains, that is the time occurrences of action potentials emitted by neurons. Our present work focuses…
We study the asymptotic behavior of short cycles of random permutations with cycle weights. More specifically, on a specially constructed metric space whose elements encode all possible cycles, we consider a point process containing all…
We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the…
Poisson restart assumes that a stochastic process is interrupted and starts again at random time moments. A number of studies have demonstrated that this strategy may minimize the expected completion time in some classes of random search…
A property of data which is common across a wide range of instruments, markets and time periods is known as stylized empirical fact in the financial statistics literature. This paper first presents a wide range of stylized facts studied in…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…
The financial markets are understood as complex dynamical systems whose dynamics is analysed mostly using nonstationary and brief data sets that usually come from stock markets. For such data sets, a reliable method of analysis is based on…
Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules,…
In this paper we propose a bivariate generalization of a weighted indexed semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that financial returns are described by a weighted indexed semi-Markov chain…
In Financial Signal Processing, multiple time series such as financial indicators, stock prices and exchange rates are strongly coupled due to their dependence on the latent state of the market and therefore they are required to be jointly…
We consider the moving particle process in Rd which is defined in the following way. There are two independent sequences (Tk) and (dk) of random variables. The variables Tk are non negative and form an increasing sequence, while variables…
We describe stochastic calculus in the context of processes that are driven by an adapted point process of locally finite intensity and are differentiable between jumps. This includes Markov chains as well as non-Markov processes. By…
Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the…