Related papers: Long-range memory model of trading activity and vo…
We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest…
We introduce a stochastic price model where, together with a random component, a moving average of logarithmic prices contributes to the price formation. Our model is tested against financial datasets, showing an extremely good agreement…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics…
In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval,…
In this paper we discuss a concept of dynamic memory and an application of fractional calculus to describe the dynamic memory. The concept of memory is considered from the standpoint of economic models in the framework of continuous time…
The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Marcus stochastic delay differential equations (SDDEs) are often used to model stochastic dynamical systems with memory in science and engineering. Since no infinitesimal generators exist for Marcus SDDEs due to the non-Markovian property,…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of…
The liquidity risk factor of security market plays an important role in the formulation of trading strategies. A more liquid stock market means that the securities can be bought or sold more easily. As a sound indicator of market liquidity,…
This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, $x(t)$, depends on the stochasticity of the return on…
Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…